Jack Balkin is Knight Professor of Constitutional Law at Yale Law School, and unintended proprietor of the best law blog. This week, he said President Obama already has effectively begun using the Fourteenth Amendment to prevent a government default.
Obama has already told bond holders that there will be no default on bonds. He plans to use existing revenues to pay off interest on the debt and other vested obligations. This is required by section 4 of the Fourteenth Amendment.  Whatever he says in public, his lawyers have almost certainly told him something like that. But that means less money for other government services, including social safety net programs like Medicare.
So we'll see a partial government shutdown once the government runs out of other options.
Which would prevent a default, and which also would put additional pressure on Congress to raise the debt ceiling as the government goes into a widening shutdown. No Medicare payments. No help for military veterans. With Congress fully responsible until it does what it always had done until now.

Of course, this also revisits the budget debate from last year, when the president's most ardent supporters argued that he shouldn't follow President Clinton's lead in allowing the Republicans to shut down the government rather than pay their ransom demands. Of course we wouldn't be here at all if the president had forced the Republicans' hand then. But we are here, and the president may now have to choose a partial and spreading government shutdown as preferable to the economic chaos that would be a default; according to Balkin, he really has no choice.
What if Congress still won't budge after months of government shutdown? Even then,  Obama has to wait until the markets threaten to implode and the validity of the public debt is put into question.  Then Section 4 says comes into play again, and, in that extraordinary set of circumstances, would require him to act to prevent a meltdown.
In other words, there are options other than trillions in budget cuts during a deep recession, cutting Social Security, Medicare and/or Medicaid and/or other accessions to Republican demands. Keep that in mind, as this concocted "crisis" resolves itself, one way or another. The bottom line, according to Balkin, being that there will be no default. Because the president has no choice but to prevent one.