I personally find Jesus' soteriological message to be a lot more subtle than what people of his time (or even now for that matter) expected—for those with 'little dust in their eyes,' as Brahma Sahampati would say.
Starting with the Gospel of Matthew, for instance, the Sermon of the Mount is a perfect example of Jesus turning people's expectations on their heads. Many were waiting for a warrior king in the line of David who'd lead them out of oppression through strength and might and military genius. But here we have the 'messiah' preaching the importance of right action and harmlessness, especially forgiveness and righteous (skillful) deeds, rather than shouting battle cries. Much of it reminds me of ideas and teachings found in the Pali Canon.
One parallel is the way Jesus points towards the importance of our intentions, teaching that anger itself is as much of a sin as acts of anger: "You have heard that it was said to your ancestors, 'You shall not kill; and whoever kills will be liable to judgment.' But I say to you, whoever is angry with his brother will be liable to judgment" (Mt 5:21-22). Similarly with thoughts of lust: "You have heard that it was said, 'You shall not commit adultery.' But I say to you, everyone who looks at a woman with lust has already committed adultery with her in his heart" (Mt 5:27-29). The focus is always on cultivating intentions of helping those in need, being humble, enduring wrong-doing, and not harming others. And the Buddha is well-known for the great emphasis he places on our intentional actions (kamma).
Jesus on honesty is also similar to the Buddha. Jesus says your speech should always be truthful so that there's no need for oaths, to, "Let your 'Yes' mean 'Yes,' and your 'No' mean 'No.' Anything more is from the evil one" (Mt 5:33-37); the Buddha says, "For the person who transgresses in one thing, I tell you, there is no evil deed that is not to be done. Which one thing? This: telling a deliberate lie" (Iti 25). Truthfulness, it would seem, is an integral part of the holy life.
Jesus admonishes his followers not to act righteously for attention and praise (e.g., Mt 6:1-6), but quietly, out of love and humility (i.e., right intention). And I see a striking resemblance between Jesus' words on loving one's enemies in Mt 5:43-45 and the simile of the saw in MN 21, both teachings stressing the importance of harmlessness, patience, and endurance.
When Jesus talks about 'treasure in heaven,' I interpret it as referring to both renunciation of sensuality that's often pursued by contemplatives and the treasure of skillful deeds done out of a heart well-developed in loving-kindness, compassion, sympathetic joy, and equanimity, the four sublime attitudes (brahma-vihara, literally 'divine abodes'):
Do not store up for yourselves treasures on earth, where moth and decay destroy, and thieves break in and steal. But store up treasures in heaven, where neither moth nor decay destroys, nor thieves break in and steal. For where your treasure is, there also will your heart be. (Mt 6:19-21)
And when Jesus says, "Stop judging, that you may not be judged. For as you judge, so will you be judged, and the measure with which you measure will be measured out to you" (Mt 7:1-2), I can't help but to be reminded of the Buddha's fifth subject for frequent reflection, "I am the owner of my actions, heir to my actions, born of my actions, related through my actions, and have my actions as my arbitrator. Whatever I do, for good or for evil, to that will I fall heir" (AN 5.57).
Each offers a version of the golden rule. Jesus at Mt 7:12:
Do to others whatever you would have them do to you. This is the law and the prophets.
And the Buddha at SN 55:7:
What is displeasing & disagreeable to me is displeasing & disagreeable to others. How can I inflict on others what is displeasing & disagreeable to me?
Comparing Mt 7:15-23 to AN 4.192, both Jesus and the Buddha seem to agree that you'll know a good disciple/teacher from a bad one by their deeds, not simply their words or reputation. And they both stress the positive aspects of renunciation and having a strong commitment to ethical action and moral precepts, suggesting that these are the foundations to living a life that goes against the current of worldly passions for the sake of a greater happiness, of living heedfully, steadfastly, and with wisdom—Jesus in places like Mt 7:24-29 and Mt 16:24-27, and the Buddha in places like AN 4.184 and AN 9.41. It's not surprising, then, that Jesus' early disciples were a lot like the Buddha's monastics, wandering mendicants who even gave up filial obligations (e.g., Mt 8:18-22 vs. Sn 1.3 or DN 2).
Another passage on intention and action, while simply put, has deep implications, and is reminiscent of the beginning of the Dhammapada. In an admonishment to the Pharisees after they accuse him of demonic consortion, Jesus says:
Either declare the tree good and its fruit is good, or declare the tree rotten and its fruit is rotten, for a tree is known by its fruit. You brood of vipers, how can you say good things when you are evil? For from the fullness of the heart the mouth speaks. A good person brings forth good out of a store of goodness, but an evil person brings forth evil out of a store of evil. I tell you, on the day of judgment people will render an account for every careless word they speak. By your words you will be acquitted, and by your words you will be condemned. (Mt 12:33-37)
Likewise, the first two verses of the Dhammapada make a similar point, I think:
Mind [aka, heart] precedes all mental states. Mind is their chief; they are all mind-wrought. If with an impure mind a person speaks or acts suffering follows him like the wheel that follows the foot of the ox.
Mind precedes all mental states. Mind is their chief; they are all mind-wrought. If with a pure mind a person speaks or acts happiness follows him like his never-departing shadow. (Dhp 1-2)
One passage that especially stands out to me in Matthew regarding the importance of intention, which almost identically mirrors the Buddha's point in Sn 2.2, is where Jesus says to his disciples:
Don't you see that whatever enters the mouth goes into the stomach and then out of the body? But the things that come out of a person's mouth come from the heart, and these defile them. For out of the heart come evil thoughts—murder, adultery, sexual immorality, theft, false testimony, slander. These are what defile a person; but eating with unwashed hands does not defile them. (Mt 15: 17-20)
I found this rather surprising since I'd always assumed that Jesus had a rather rigid approach to Mosaic laws, i.e., "Do not think that I have come to abolish the law or the prophets. I have come not to abolish but to fulfill" (Mt 5:17). But time and again, Jesus is seen doing something that seems contrary to the law even though he says he's come to fulfill it. Here's Jesus rebuking the Pharisees and their rigid approach to living a spiritual life, saying that it's really all about our intentions, not necessarily following the letter of the law. There's Jesus forgiving someone for their sins, and challenging those without sin to cast the first stone at the accused (John 8:1-11), etc.
What this ultimately says to me is that Jesus' version of fulfilling the law is very different from what many assume, with much of the means of fulfillment containing levels of Dhamma — albeit presented in a different social, religious, and cultural context — with God representing much of what Buddhists understand as Dhamma (kamma = moral commandments of God, ripening of actions = judgment of God, the deathless/unconditioned = timelessness/transcendence of God, etc.). Perhaps this is why Jesus says, "Whoever has seen me has seen the Father [God]" (John 14.9) and the Buddha says, "he who sees me sees Dhamma" (SN 22.87).
And then there's the salvific power of love. In Richard Gombrich's book, What the Buddha Thought, for example, he mentions that, while the idea of loving-kindness (metta) being salvific is often neglected in Theravada — i.e., the general consensus traditionally being that the four brahma-viharas themselves only lead to rebirth in the heavenly Brahma realms and not nibbana, the end of stress/suffering (dukkha) and awakening to ultimate reality — there are texts in the Pali Canon extolling kindness and how it can lead to enlightenment. One is the Metta Sutta (found at Khp 9 and Snp 1.8), which begins with extolling kindness towards the world, and climaxes with this passage:
Towards the whole world one should develop loving thoughts boundless: upwards, downwards, sideways, without restriction, enmity or rivalry. Standing, walking, sitting or lying, one should be as alert as possible and keep one's mind on this. They call this divine living in the world. Not taking up ideas, virtuous with perfect insight, by controlling greed for sensual pleasure one does not return to lie in the womb. (Gombrich's translation)
He notes that, "This conclusion to the poem surely corroborates that the whole poem is about how one may become enlightened. Moreover, it is natural to interpret 'not returning to lie in the womb' as meaning that one will have escaped altogether from the cycle of rebirth, which is to say that one will have attained nirvana [i.e., nibbana]" (87). Of course, he's careful to point out that the poem doesn't state kindness alone will produce salvific results, and that it mentions other qualities of great importance (e.g., insight and self-control), but then he brings up Dhp 368:
The monk who dwells in kindness, with faith in the Buddha's teachings, may attain the peaceful state, the blissful cessation of conditioning. (Gombrich's translation)
Or an alternate translation from Acharya Buddharakkhita:
The monk who abides in universal love and is deeply devoted to the Teaching of the Buddha attains the peace of Nibbana, the bliss of the cessation of all conditioned things.
Gombrich concludes this passage is "saying that kindness is salvific, and it is surely no coincidence that the term for nirvana, 'the peaceful state', is the same as the one used at the opening of the Metta Sutta" (87).
So it's quite possible that love is a path to nibbana, and as such, I'm inclined to agree with Gombrich that it can be salvific in the proper context. It's one of the ten perfections, after all, which are not only the skillful qualities one develops as one follows the path to nibbana, but the basis of the path to full Buddhahood as well. And this, I think, accords well with passages in the Gospels such as, "You shall love the Lord, your God, with all your heart, with all your soul, and with all your mind. This is the greatest and the first commandment. The second is like it: You shall love your neighbor as yourself" (Mt 22:36-40), "Whoever is without love does not know God, for God is love" (John 4:8), and, "I give you a new commandment: love one another. As I have loved you, so you also should love one another. This is how all will know that you are my disciples, if you have love for one another" (John 13:34-35).
Similarities can also be found in their respective contemplative techniques. Theravadin mindfulness meditations utilizing the breath or a meditation word, especially those found in the Thai Forest Tradition, are similar to the Orthodox hesychasm prayer, popularized most famously in the 19th century Russian text The Way of the Pilgrim; the form of prayer found in The Cloud of Unknowing, written sometime in the 14th century; and the more modernized version based on The Cloud of Unknowing called centering prayer.
And there are other commonalities, like confession, where one reflects on and acknowledges their sinful (unskillful) actions by giving into anger, greed, envy, lust, etc., gains advice from a spiritual teacher (priest), and makes a commitment to try and not commit those acts again. And this is not unlike the Buddha's advice to Rahula in MN 61, i.e., reflect on your actions, and if they cause harm, consult with someone wise, and try to not repeat said actions in the future. The Buddha's monastic sangha does something similar, where certain Vinaya offenses require monks to confess them, and there's also a tradition where monks recite the rules and confess to one another any faults committed and ask forgiveness of their fellow monastics during the uposatha. Or the similarity between the Christian practice of dying to self vs. the Buddhist teachings on not-self—each designed to release our clinging-attachment to the appearances of ephemeral, conditioned phenomena (what Buddhism might term 'globs of foam,' or in Biblical terms is characterized by phrases such as, "for you are dust, and to dust you shall return") and disrupt the fabrication of self-identification view and existential egoism, thereby opening ourselves up to a direct inner experience of God/Dhamma and realizing our true nature.
So in closing, after spending years living and breathing these traditions and finding a surprising amount of compatibility, I believe that one can find numerous elements of Dhamma — truth or ultimate reality — within Jesus' teachings and Christianity in general. Most Buddhists would likely disagree that following Jesus can lead to full awakening, but I think a fair number would at least agree that one can generate good kamma and achieve happiness and favourable rebirth (whether literal or psychological) by following his example. And I suspect one can potentially achieve even more, be it union with the ground of being or nibbana itself.