Real oldheads remember the short-lived Tucker Carlson (yes)/Bill Press show on CNN. It wasn't a great show, precisely, but it did provide some mild mocking of the conventions of the basic cable news political show of the time. A kind of "yes what we do is a bit ridiculous" attitude about the whole thing.
And the name itself - The Spin Room - referred to the post-debate efforts by political operatives to convince journalists that THIS was best zinger, and THAT was a damning, campaign-ending gaffe.
Not much that happens in a debate matters all that much until news outlets start running it on a loop, and the spin room is how you get them to do that.
Things have changed a bit since then, but not so much.