Is it possible that the words of Jesus, as written in the Bible, are not infallible?

Yes, they've been translated and edited too many times.  But in the broad strokes, the Bible still holds together very well.

The words of God, and therefore Jesus, are certainly infallible. However, the interpretation of His words by humans are certainly not infallible, except by the one Church He founded, to which Jesus promised "The Holy Spirit will guide you into all truth", and "Whatsoever you bind upon Earth is bound in Heaven", and "He who hears you hears Me". Which is why that one Church remains one in belief, one in reaching, one in worship, one in biblical understanding throughout the world after 2,000 years, while those who have defected from His Church have fragmented into more than 6,000 denominations in a few hundred years, the teaching of each one contradicting the teaching of the others.

If they are infallible then why did Jesus have to suffer what is the equivalent of a modern day lynching?

Yes, of course that's possible.

I don't believe it to be the case

but one cannot reasonably deny the possibility.

Like what? I'm not a Christian who thinks the Bible is infallible, I don't need it to be. I want the best written source for finding out what God said and what God did. If you know a better source, tell me what it is. 

It is *more* than possible because Heaven is real. and it 

does not simply take place just because Christianity is here. 

The biblical character called 'Jesus Christ' knew that, 

but not even one of the christ-based faiths will ever admit it. 

The King James Bible is 100% perfect.  Use it.  It is infallible.  Start reading in the Book of John.  The Lord Jesus Christ is God, and He loves you.  Believing in the Lord Jesus Christ means being forgiven all sins past and future, and means going to heaven and not hell.  Death leads to immediate heaven or hell, and it is too late to be saved, after death.  All believers still sin.  See 1 John 1:8.  To be in heaven and not hell, believe in the Lord Jesus Christ, who is God and who died on the cross and shed His blood to pay for all of our sins in full, and who was buried, and who resurrected from the dead.  The only way to avoid hell is by believing in the Lord Jesus Christ, without adding any of your own works.  See Romans 4:5, 1 Corinthians 15:3-4, and John 3:16.

Is it possible that some of it has gotten and gets lost in translation? Yes. Jesus spoke in Aramaic. The Gospels are second-hand accounts, which is why there are several of them that all go over the same set events and teachings, like how you need to hear the same story from several witnesses to get a complete picture of what actually happened. Those second-hand accounts then got translated into Greek, then translated into Latin, then translated into English. 

Every time something is translated even directly from one language to another, discrepancies are unavoidable. That's because a word can have several meanings that corresponding word in another language doesn't have or because a word can nuance a meaning that no word in the language it's being translated to nuances. This becomes compounded when idioms are used since idioms convey a meaning different than the words themselves together convey and since idioms are language and culture-specific and so another language is highly unlikely to have an idiom that means the exact same thing. Then there's double-entendres. People often say things that are intended to convey two meanings, like by using a play on words or by punning, but those also are language specific, so both meanings can't be translated into a single statement. All of this being the case means that translators must try as best they can to interpret the meaning and convey that meaning in the new language as best they can, but translators are sometimes wrong and their translations sometimes unavoidably fall short because of the reasons above.  

By the way, this possibility, the possibility of translation fallibility, is why the Bible used to be only ever studied in Latin (to prevent any further possibility of translation fallibility); why the Torah and Tanakh are studied in their original language of Hebrew and why Jewish children whose first language isn't Hebrew go to Hebrew school to learn Hebrew; and why the Quran is to be studied in its original language of Arabic and why all converts to Islam are called upon to learn Arabic.

Here's an example: There are many Bible verses that refer to sheep and wool, but what if there is no word for sheep in the language the Bible verse is being translated to because sheep are not indigenous to where that language is spoken, so a translator has to hope that there's some kind of domesticated animal that is akin to sheep, that is docile, that flocks, that has coats harvested and used like wool, and whose coats are white for all of those references to make sense in translation, which is a pretty tall order to fill, often an impossible order to fill.

The entire bible is a fictional train wreck.

Have you not read it?

There's nothing possible or even probable. Jesus's words in the Bible are literary fiction because he never existed.