I've always sensed that Colbert loves Prine's work because he has him on the show so often. And singing a duet with him confirms that. But what really sets my certainty is stone is a moment -- actually a couple moments, but one in particular -- that make this A Sure Thing. I'm not even going to give a heads-up when to watch so that you don't miss it. You won't miss it.
What I've wondered if Colbert just has a general appreciation of Prine which has come over time, or if it stems from when Colbert went to Northwestern University and then worked in Chicago at Second City. John Prine is such an icon there, part of the folk-god triumvirate in the city with Steve Goodman and Bonnie Koloc, and though their peak was before Colbert came to the area, the aura has lingered for decades, even to this day. In any event, wherever his love of John Prine's work comes from, it certainly shows here.
And as long as I'm at it, I may as well also post the song I had been looking for. My search came about because of seeing a tweet from Trump that had the American flag washing over everything, and I wanted to complement with Prine's great "Your Flag Decal Won't Get You Into Heaven Anymore."
For that, I tracked down his original recording of the song written in 1968. Here though I found a more appropriate version. It's live in concert (though audio only) from 2010, and he talks about writing the song about Viet Nam (when he was a mailman in Chicago), retiring the number, but bringing it back because of "the previous administration," which would be George W. Bush.