In case you have not been paying attention, there is growing sentiment in favor of the Platinum Coin Seigniorage (PCS) and the Trillion Dollar Coin.
Here are two solid posts on it, one by economist Paul Krugman, the other by Philip Diehl, former director of the US mint .
The crux of the issue is that the debt ceiling, created by legislation of our congress, is inconsistent with the powers enumerated in the constitution, specifically the fourteenth amendment.
Here is the relevant sentence in section 4, of the 14th amendment of the US constitution.
Section 4. 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.
Here is the Wikipedia discussion of the issue, somewhat dated.
The issue of what effect Section 4 has regarding the debt ceiling remains unsettled. Legal analyst Jeffrey Rosen has argued that Section 4 gives the President unilateral authority to raise or ignore the national debt ceiling, and that if challenged the Supreme Court would likely rule in favor of expanded executive power or dismiss the case altogether for lack of standing. Erwin Chemerinsky, professor and dean at University of California, Irvine School of Law, has argued that not even in a “dire financial emergency” could the President raise the debt ceiling as “there is no reasonable way to interpret the Constitution that [allows him to do so]”.