I'm seeing people way too confident in their view of what the "correct" constitutional resolution to a breach of the debt ceiling would be, so I want to emphasize how hard the problem is.
In normal times:
1. The president arbitrarily deciding not to fund a program, or to fund it less than congress wants, is a massive usurpation of congress's powers to legislate and to spend money to promote the general welfare. What's more, in normal times the president not giving a welfare recipient money because he wants to use it for a different purpose would be a due process violation. Same with not paying out a contract. Not paying out money to a creditor or pensioner would be a fourteenth amendment section 4 violation. All totes unconstitutional.
In short, the Prez simply deciding he is going to arbitrarily choose how to spend America's funds is crazy unconstitutional and a crazy infringement on congress's power.
2. In normal times, the president deciding, without constitutional approval, to raise some funds would be crazy unconstitutional. Congress has the power to tax or borrow, the President doesn't. This is, like, separation of powers 101 stuff, you guys.
Ok, so all those things are clearly true. But people don't seem to recognize that they are both true? Matt Yglesias emphasizes point 1 and then says "so clearly the president should just breach the debt ceiling." Laurence Tribe emphasizes point 2 and then says "so clearly the president prioritizing payments is the lesser of two evils."
But no, guys, neither of these are clearly a lesser evil. They are both terrible. Which one of these terrible and unconstitutional things might be, due to circumstances, constitutional in this case is a hard question.
That said, these are what I think the two correct answers might be, from most likely to least likely, but I am still very unsure about either:
1. This is clearly a failure of the constitution and there is no "correct" way out. So long as he limits his unconstitutional looking actions to narrowly solving the crisis, either by prioritizing payments or by borrowing more, how the President resolves two contradictory and equally grave constitutional obligations is a political question and the courts shouldn't review it.
2. Both arbitrarily choosing what to fund and borrowing money to cover what congress wants to spend seize congressional power in a (normally) hideously unconstitutional way, but arbitrarily prioritizing payments has the added problem of violating the due process rights of the people owed those payments, since the amount of due process you are owed when you are deprived a legal benefit is normally greater than "the president doesn't prioritize your program and really wants to spend the money elsewhere." So, given the extra constitutional problems prioritizing payments brings, go with borrowing more.
A simple "he has to do it because of the fourteenth amendment says you have to honor debt" argument, by the by, is likely wrong. The fourteenth amendment makes a distinction between debts and obligations, and only says that the validity of the former cannot be questioned. In the fourteenth amendment "debt" is probably stuff like money the government owes to creditors, money owed to pensioners, and payment for services rendered. I'm pretty sure you could pay all of that out of the revenue we collect.