Even if you reject most or all of the Bible can you reject even what Jesus said during his short life?
The Bible is an ancient document. It was written by numerous different authors from various walks of life and over a period of hundreds of years. Like any ancient document, the reliability may come into question.
The reliability of the Bible is very well established, as ancient documents go. There are more supporting manuscripts for the Bible than for any other ancient document. That includes the works of Greek philosophers, which are routinely taught verbatim in schools and universities as fact.
In the case of Jesus' words, we have four gospels to document the primary points of His 3-year ministry. These four separate accounts originate from four of the twelve disciples. While these accounts don't all say exactly the same things, they agree enough that books have been written discussing the "harmony of the gospels." Some details appear in one version, but are omitted from another. One may take a very literal view of the events, while another may look at the words and actions from a more human perspective.
Just as we do today, the story will be presented differently depending on who is telling it.
The reason I believe what was said were the actual words of Jesus, isn't because of the external historical references, or the internal verifications in other parts of the Bible. It's also not because of the overwhelming MSS evidence that it was said or the archeological findings that seem to back up Jesus' words. The primary reason I accept it is because I have faith.
Faith is being absolutely sure of things you cannot see, or touch or hear. I have faith that if I climb on board an airplane, that it will carry me safely to my destination. I cannot see the air, which is the media enabling the plane to fly. I have no absolute evidence that it will be there during the entire flight to prevent us from falling out of the sky. However I do have faith in the pilots and engineers, that they have worked all of that out.
In the same way, I have faith that the various scribes over the many hundreds and even thousands of years, have been diligent, believing that this is canon, and to copy it letter by letter, to insure that it remains accurate.
I also have faith that if there is a God who can speak the entire universe into existence, that He can much more easily preserve the text of a document over the course of human history.
There's no amount of hard physical evidence to convince someone that Jesus is absolutely real or that the words we have are His. But there's definitely enough faith to cause many people to be certain of it...