The Constitution vests in Congress the authority to take on debt for the United States government. The 14th Amendment stipulates, "The validity of the public debt of the United States, authorized by law, including debts incurred for payment of pensions and bounties for services in suppressing insurrection or rebellion, shall not be questioned."
So, what if Congress refuses to authorize the additional borrowing necessary to pay the debts already incurred?
Ever since the debt ceiling law was established in the World War I era, presidents and members of Congress have taken it as given that the congressionally imposed limit is constitutional, as an extension of its authority to incur debt. But in the present situation we have a Congress that cannot agree on the measures necessary to pay off debts that Congress has already incurred. Congress will thus, by inaction, call into question the "validity of the public debt of the United States." They would be in direct violation of the 14th Amendment's stipulation.
This puts the President in a difficult position. If he defers to Congress and accepts a default on the debt, with its attendant catastrophic economic consequences, he would be a party to Congress' violation of the 14th Amendment. If he invokes the 14th Amendment, and his oath that he will "to the best of my ability, preserve, protect and defend the Constitution of the United States," he would simultaneously challenge the prerogative of Congress to incur debt for the United States. Which part of the Constitution prevails here?
The problem is that Congress has (mostly since 2001) incurred massive debts, that it cannot agree on budget cuts or tax increases to reduce those debts, and that it also cannot agree to pay the debts. Raising the debt ceiling amounts to authorizing the Treasury to incur more debt, for the purpose of paying debts already incurred; or in other words, to assure that the legally authorized public debt "not be questioned."