They're [Congress] not trying to circumscribe the President's regal powers, they're trying to circumscribe, the White House argues, his Presidential powers... what they're not permitted to do is to appropriate funds and then tie the Commander-in-Chief's hands with respect to how to deploy those troops and how to conduct those military missions.
I don't think this is what the White House is arguing at all, although I'm sure they're happy to have their allies chat it up. Here's the President at his last press conference:
Q When Congress has linked war funding with a timetable you have argued micromanagement. When they've linked it to unrelated spending, you've argued pork barrel. But now there's talk from Harry Reid and others that if you veto this bill, they may come back and just simply cut off funding. Wouldn't that be a legitimate exercise of a congressional authority, which is the power of the purse?
THE PRESIDENT: The Congress is exercising its legitimate authority as it sees fit right now. I just disagree with their decisions. I think setting an artificial timetable for withdrawal is a significant mistake.
For whatever reason, the White House has already ceded the constitutional point.