That's called "promotion", or "endorsement".

It's not hard to ferret out the numerous lies in David Barton's book, but you need to own it, and also to have a copy on hand of a book by author Chris Rodda - Liars For Jesus: The Religious Right's Alternate Version of American History (link to free PDF of book). Or, you can watch this 2-hour video of Rodda patiently walking through the tedious process of debunking lies from one of the chapters of Barton's book. by referencing her debunking of Barton lies contained in her own Liars For Jesus book.

For a more general treatment critical of Barton's work, see this extended report from People From The American Way, Barton's Bunk: Religious Right `Historian' Hits the Big Time in Tea Party America.

Because Stewart did not challenge any of the specifics of Barton's book during the ensuing interview, many viewers will at least conclude that even if Jon Stewart doesn't personally endorse David Barton's book, that the book is at least a reputable work of history rather than a tendentious work packed with contrived history lies designed to destroy the separation of church and state and advance Christian nationalism.

Some of those viewers, well-meaning Americans, will buy the book, and some of the responsibility will for that will lie with Jon Stewart. This raises the question: does Jon Stewart bear any responsibility for what's on his show? After all, it's comedy, right?

But if The Daily Show is comedy, isn't the role of a comic to call out lies, indeed to skewer them - rather than promoting them, and their messenger, to the nation as being somehow valid or mainstream?

That was the most painful part of Barton's 2nd appearance on The Daily Show - Barton won the debate with Stewart before it even began. Barton won simply by being onstage with Stewart, and he won from the moment Stewart held up Barton's new book.

It's probably a pitfall of success. Stewart, a brilliant comic and conversationalist, can't seem to admit that he's overmatched on David Barton's own chosen turf. Barton is a true specialist - he specializes in elaborately constructed history lies, part of a vast, growing body of pseudo-history by Christian nationalist authors which serves to politically mobilize the religious right.

There's a lot to learn, and perhaps John Stewart will one day acknowledge that - by inviting on his show someone who, as does Rodda, specializes in rebutting Barton. Try as he may, Stewart can't do everything, and in this particular case his attempt to do so has real political consequence. I doubt Jon Stewart would be happy with the idea that he's just helped advance the Christian dominionist movement, but that is the unfortunate reality.  

As author Frederick Clarkson writes, in a trenchant History is Powerful: Why the Christian Right Distorts History and Why it Matters,

"The notion that America was founded as a Christian nation is a central animating element of the ideology of the Christian Right. It touches every aspect of life and culture in this, one of the most successful and powerful political movements in American history. The idea that America's supposed Christian identity has somehow been wrongly taken, and must somehow be restored, permeates the psychology and vision of the entire movement. No understanding of the Christian Right is remotely adequate without this foundational concept.

But the Christian nationalist narrative has a fatal flaw: it is based on revisionist history that does not stand up under scrutiny. The bad news is that to true believers, it does not have to stand up to the facts of history to be a powerful and animating part of the once and future Christian nation. Indeed, through a growing cottage industry of Christian revisionist books and lectures now dominating the curricula of home schools and many private Christian academies, Christian nationalism becomes a central feature of the political identity of children growing up in the movement. The contest for control of the narrative of American history is well underway."