On biblical infallibility...

Where does this idea come from?

P1: God is infallible.
P2: God wrote the Bible.
C1: The Bible is infallible.

yes, I understand what the idea is, but that isn't the question. Where did the idea that the bible is infallible originate?

... the scripture cannot be broken;

A combination of the above, and multiple scriptures ... "All Scripture is God-breathed ...", Jesus making arguments that rely upon the very letters and less of certain passages being exact, there are many passages that speak to this sort of thing.

Now, no one (at least no serious scholar) claims infalability for the versions that we have today. We claim infalability of the original autographs. Our Bibles today are infallable in so much as they adhere to those originals. There have been a couple of minor copyists errors here and there that we know of. However, the art and science of studying and comparing the tens of thousands of manuscripts we have give us a very high degree of assurance that what we have is very nearly what was originally penned. For instance, in the New Testament, there is question or debate on less than 2% of the text, and those passages that are somewhat in question, even if every single one were removed, would not endanger or alter or cause us to call into questioning any single orthodox teaching of the historic Christian faith.

The problem I see with the bible being used to support the idea (well, aside from being circular logic) is that those passages would have been referring to the scripture as it stood back then. Paul was certainly not meaning to claim that his letter to Timothy amounted to scripture. Even jumping forward to the choosing of the books for the new testament at the council of Nicea, they made no claim to infallibility in their selection.

Peter in 2 Peter claims that Paul's writtings were Scripture though ...