The current selection of 66 books that make up the bible as used by most protestants (as far as I know, the Eastern Orthodox and Roman Catholic bibles contain slightly different selections of books) was not finalised until a few hundred years after they were written.
So why is it that many Christians will use the text of some of those 66 books to claim that the contents of all 66 (and only those 66) books are divinely inspired?
2 Timothy 3v16 speaks of 'all scripture' but how can we assume that this refers to the current selection of 66 books? At the time he was writing Paul (or whoever) had a much smaller selection of 'scriptures' which did not include any of our current new testament.
Jesus frequently used phrases like 'my words will never pass away' and so on, but if you compile all of the things that Jesus said from the gospels, you end up with only a few hours worth of sayings. In my opinion, it is these sayings that we, as Christians should seek to follow. Of course, some doubt if Jesus Himself actually said all these things, but even assuming that He did, the sum total of all His Words is tiny compared to the entirity of the bible. When Jesus speaks of 'my words' I don't believe that He meant everything in the bible - He just meant the things He was saying.
I can't believe that everything in all 66 books is the inspired and infallible Word of God (see, for example, the story of Noah and the Ark), but I can believe that most of the words attributed to Jesus are things He said, or are interpretations of the things He said as understood by His disciples (e.g. the things Jesus apparently says in John's gospel are different to what He says in the other three - this is generally understood as being John's interpretation of what Jesus meant, rather than a word-for-word account of what he actually said).
We know that the Jews couldn't live up to the 'burden' of the old testament law (Acts 15:10). Neither can we. Thankfully, as Christians we only need to follow Christ and His words, and this is something we can manage.