The fact that Grover Norquist of all people will begrudgingly support Mitch McConnell's Plan Z to avoid debt default makes plenty of sense when you stop thinking of Grover as an ideologue, and consider his incentives as a conservative power player.
His main goal, above all else, isn't to cut spending. Not even close. His real priority is to maintain influence in Republican politics. Way below that, somewhere alongside not losing the ability to speak out loud, he wants to keep taxes low. Those two things are related, but they're not the same, and they don't point to any real conviction on what should be first on the chopping block.
Right now, whether he knows it or not, President Obama has a chisel resting at the most vulnerable point of contact between Grover and the GOP, and, if he's willing to commit, a hammer hovering threateningly above it.
He knows Congress has to raise the debt limit, and he seems to truly believe Obama won't let them do it without offering up new tax revenue -- and that would mean forcing Grover into early obsolescence. Taking that as a given, would he rather see the GOP cave in a way that renders him meaningless, or cave in a way that preserves the power of the "pledge." I totally understand his thinking here.