Honestly, it's just as likely that the Biden administration will have to mint a platinum coin.
I'm not saying a final minute deal can't be struck, but what you're suggesting isn't very realistic. The problem is McCarthy sold his own ass to the "Freedom" Caucus to get elected Speaker by the narrowest of margins, and that's all he fucken cares about. They do not care if the economy tanks, because they mostly don't care about the middle class and many are fixated on the dream of "starving the beast" (the federal government, except the military of course).
I guess there's a universe where if Sen. McConnell leans hard enough, you could find a handful of moderate House members to cross the aisle and pass a compromise bill. But there are almost no moderate House GOP members left; and outside of obstruction, Mitch doesn't really have powers of persuasion. You can make the case that if push came to shove, McCarthy cares more about being Speaker than averting a completely manufactured economic crisis. If he even tries to pass a reasonable bill (let's say Dems offer up some minor concessions), he knows Freedumb will kick his ass to the curb.
You might be right that the GQP may ultimately cave days or weeks after a damaging default has already occurred, but in light of the looming June 1st deadline, their list of wants is completely unreasonable when compared to prior clean debt limit increases. FFS look at the U.S. Chamber of Commerce claiming that the executive branch invoking the 14th Amendment is as bad as an actual default: