Everything Robert said. 

But a couple of further pessimistic thoughts, with respect to the Gospels more than the Paulines:

It isn’t even clear to me that there was a single autograph. Even today, works can go through multiple editions (there may be several versions an author circulates privately as he continues to work on it, versions which sometimes circulate quite widely; then there are sometimes even multiple “final”, printed editions). 

Adding to that is the more general question, Who is the author? Who is a redactor (does he count as an author)? Who is just a scribe taking liberties? I think it is common to recognize, especially in some of the gospels, that there are sometimes several voices at work or several layers in the text (John and Luke are prime examples). 

All the evidence suggests that the earlier we go, the less reliable transmission was and the freer people were with changing the text. And the earliest period is precisely where we have the fewest data. Thus when the texts were most in flux is when we have no direct view of the process. Indeed it seems that in the earliest stages the texts were, one might say, living documents.

So not only is it not clear how we could recover the pristine original with the data we have, it isn’t even clear that there is a single pristine original to recover.