From a Constitutional scholarship angle, GOP Representative Mike Lee is pretty accurate when he says that Timothy Geithner can't ignore the debt ceiling:
By the way, NPR's Planet Money did a great job explaining the history of the debt ceiling. If you follow the history, you see that it used to be that every single piece of debt had to be passed in an act of Congress. The debt ceiling is Congress' way of delegating its powers to the executive branch, within the limits of the debt ceiling. But just because the powers are delegated (in the same way that the War Powers Act temporarily delegates the ability of the President to deploy troops in "hostilities" within certain limits) doesn't mean that the sole power now exists with the executive.
That said... I really hope the debt ceiling goes up soon.