It's actually a popular book written by a well respected scholar that summarises the current consensus position.
I know who he is and overnight I'm (albeit superficially) read the most relevant section of the 'for popular audience' Misquoting Jesus, but also his more scholarly text 'The New Testament - a Historical introduction to the Early Christian Writings.
Having done so I don't think that he is either claiming that we can come close to the real original text (the so called autograph) nor that there is a consensus amongst scholars as to whether you can. In reality he is talking about ascertaining which of the earliest available extant text and fragment is most likely to accord with earlier, but lost, versions - which of course may not be close to the original version.
So on the former the 'headline' of the original is typically caveated by oldest or earliest attainable version - so at the start of chapter 5 we have:
"In this chapter we will examine the methods that scholars have de vised to identify the "original" form of the text (or at least the "oldest attainable" form) and the form of the text that represents a later scribal alteration."And on consensus he is clear that many scholars believe it to be impossible to get further back that the extant fragments etc we have:
"In fact, it is such an enormous problem that a number of textual critics have started to claim that we may as well suspend any discussion of the "original" text, because it is inaccessible to us."In terms of timelines he covers the period from original writing to about 1500 - so in that context first half of 2nd century is early and likely earliest attainable version - but I'm talking about changes in the decades from original writing to that point. I don't think he is really claiming that you can reach all the way back, but that you can make judgements about those early fragments and texts most likely to be similar to earlier, but lost versions - but these may themselves be many generations (and changes from the original).
He actually illustrates the intractable problem very well using the example of Paul's letter to the Galatians (see from p58); the earliest version we have is from about AD200. He point out that even at the very earliest stage a scribe working directly with Paul may have produces several versions - and may have produced the letter from direct dictation or by taking basic points and filling in the rest:
"Now, if Paul dictated the letter, did he dictate it word for word? Or did he spell out the basic points and allow the scribe to fill in the rest? Both methods were commonly used by letter writers in antiq uity.16 If the scribe filled in the rest, can we be assured that he filled it in exactly as Paul wanted? If not, do we actually have Paul's words, or are they the words of some unknown scribe? But let's suppose that Paul dictated the letter word for word. Is it possible that in some places the scribe wrote down the wrong words? Stranger things have happened. If so, then the autograph of the letter (i.e., the origi nal) would already have a "mistake" in it, so that all subsequent copies would not be of Paul's words (in the places where his scribe got them wrong)."And a couple of paragraphs later:
"What survives today, then, is not the original copy of the letter, nor one of the first copies that Paul himself had made, nor any of the copies that were produced in any of the towns of Galatia to which the letter was sent, nor any of the copies of those copies. The first reasonably complete copy we have of Galatians (this manuscript is fragmentary; i.e., it has a number of missing parts) is a papyrus called P46 (since it was the fortysixth New Testament papyrus to be catalogued), which dates to about 200 C.E. That's approximately 150 years after Paul wrote the letter. It had been in circulation, being copied sometimes correctly and sometimes incorrectly, for fifteen decades before any copy was made that has survived down to the present day. We cannot reconstruct the copy from which P46 was made. Was it an accurate copy? If so, how accurate? It surely had mistakes of some kind, as did the copy from which it was copied, and the copy from which that copy was copied, and so on.
In short, it is a very complicated business talking about the "original" text of Galatians. We don't have it. The best we can do is get back to an early stage of its transmission, and simply hope that what we reconstruct about the copies made at that stage—based on the copies that happen to survive (in increasing numbers as we move into the Middle Ages)—reasonably reflects what Paul himself actually wrote, or at least what he intended to write when he dictated the letter."
I've added some emphasis. This doesn't really seems to align with your (or his) headline claim that
"scholars are confident they have more or less reconstructed something like the original text".