When I was a Christian, I was a strong proponent of Free Grace Theology, which teaches Salvation by faith alone, and Eternal Security, in their most unqualified senses.
Of course, there are many passages in the Bible which can be called "problem texts" for these positions. How many passages? Probably a little more than 140, which is approximately the number of passages I had made articles on, during the time in which I was Free Grace.
Many of these passages come from the mouth of Jesus - specifically, the Jesus of the Synoptic Gospels (Matthew, Mark, and Luke).
For example:
Matthew 7:21-23
21 Not every one that saith unto me, Lord, Lord, shall enter into the kingdom of heaven; but he that doeth the will of my Father which is in heaven.
22 Many will say to me in that day, Lord, Lord, have we not prophesied in thy name? and in thy name have cast out devils? and in thy name done many wonderful works?
23 And then will I profess unto them, I never knew you: depart from me, ye that work iniquity.
This passage appears in Matthew's rendering of the Sermon on the Mount. Up to this point in the sermon, which begins in Matthew 5, Jesus gives moral instruction. Fulfilling this moral instruction requires diligent effort on behalf of someone. And, the passage in question suggests that if they do not do these things, they will be rejected by Jesus. A rather straightforward works-based justification, and criteria for judgment. That is the understanding of the passage that one would come away with, if they only had Matthew to read.
Jesus frequently teaches this way in the Synoptics. It is not merely the absence of any verses which would be clearly pro-Free Grace - though it is certainly that as well. Instead, the Synoptics, and the Jesus presented in them, present a pretty clear message that how one lives will determine whether or not they will go to Heaven or Hell. If they pass a sufficient-yet-undefined threshold of holiness, they are let in. If not, they will be condemned (Matthew 25:31-46). Admittedly, this theology of Jesus renders passages like Ephesians 2:8-9, and Romans 4:5, into basically meaningless doublespeak, if those authors had any awareness of what Jesus taught, or intention of representing his teachings to their readers.
But what about the Gospel of John? Though it has problem texts for Free Grace as well (e.g. John 3:36, 15:1-16), it at least appears to be more accommodating of the theology presented by a straightforward reading of Ephesians 2:8-9.
However, the Gospel of John, as discussed at length in this article, cannot be treated as a legitimate source for the words of Jesus by anyone with integrity - including by conservative Christians. Jesus in John's Gospel sounds completely different in language and theology from the Jesus of the Synoptics, while mirroring the language and theology of the author of First John (sometimes verbatim). This is because "John" essentially used Jesus as a puppet to teach his own theology.
Therefore, Free Grace Christians really aren't followers of Jesus - at least on the topic of Soteriology. Instead, they follow "John", and some of Jesus's successors. The actual person Jesus of Nazareth appears to have taught a rather straightforward works-based justification in order to get in to a very imminent Kingdom of Heaven (which did not come as he had promised). After his death, a redemption theology was created by his followers to give his execution a metaphysical meaning, when in reality, while the man was alive, he was interested in setting up a "Kingdom of Heaven", which never came.
This is why the "Gospel" switches from the announcement of the coming theocratic Kingdom in the Synoptics, to something entirely different after Jesus's execution. The movement essentially had to redefine itself in response to the totally unforeseen death of its founder. That is also why New Testament Soteriology and Eschatology are so confusing. Multiple messages are being communicated, and the details don't work out cleanly, because they are trying to re-work the death of Jesus into their theology, when Jesus himself never did. And, adding to the confusion, there are multiple factions producing material in early Christianity, and they range from extremely unclear/borderline esoteric ("John"), to messy attempts at philosophy (Paul), to some blend of Judaism with Jesus mixed in (early followers of "James", "the Judaizers", etc.).
Did Jesus teach "Free Grace Theology"? No, a responsible evaluation of the existing evidence suggests that he taught basically the opposite. The words put into his mouth by "John" are little more than "John" using Jesus of Nazareth as a puppet.
Additionally, whatever redemption theology emerged later after Jesus's execution tended more towards what could be called "Free Grace", but only very inconsistently.