President Obama might soon find himself in a quandary in which basic arithmetic prevents him from faithfully executing all of the laws Congress has passed. The debt ceiling statute prohibits borrowing enough money to make up the difference between funds in the Treasury and legal obligations to spend. Anything the president does in this case would violate some law. Indeed, anything he does would be unconstitutional because all of the relevant powers -- spending, taxing and borrowing -- belong to Congress. A limited override of the debt ceiling is the "least unconstitutional" alternative.
Additional background and detailed legal analysis here: http://hylbom.com/launchpad/wp-content/uploads/2013/01/Buchanan-Dorf.pdf