Okay, so, he's right so far as he goes. The argument that the "increased risk of defaulting" is the reason the debt ceiling would be unconstitutional is indeed stupid, for exactly the reasons he points out. Furthermore, his assessment that the president does not have the constitutional authority to borrow money on the credit of the United States is correct. But he's arguing against straw men. The real issue is this: the debt ceiling mandates a default on the full faith and credit of the united states, given certain conditions (the rising of government expenses). Not only does it make this mandate, but forcing a default under this condition is in fact the only purpose of the debt ceiling. It has no other function. In the event that it actually acts, that is what it does. This seems obviously to "question" the "full faith and credit of the United States", and must therefore be unconstitutional.Some have argued that this principle prohibits any government action that “jeopardizes” the validity of the public debt. By increasing the risk of default, they contend, any debt ceiling automatically violates the public debt clause.This argument goes too far. It would mean that any budget deficit, tax cut or spending increase could be attacked on constitutional grounds, because each of those actions slightly increases the probability of default. Moreover, the argument is self-defeating. If it were correct, the absence of a debt ceiling could likewise be attacked as unconstitutional — after all, the greater the nation’s debt, the greater the difficulty of repaying it, and the higher the probability of default.Other proponents of a constitutional deus ex machina have offered a more modest interpretation of the public debt clause, under which only actual default (as opposed to any action that merely increases the risk of default) is impermissible. This interpretation makes more sense. But advocates of the constitutional solution err in their next step: arguing that, because default would be unconstitutional, President Obama may violate the statutory debt ceiling to prevent it.The Constitution grants only Congress — not the president — the power “to borrow money on the credit of the United States.” Nothing in the 14th Amendment or in any other constitutional provision suggests that the president may usurp legislative power to prevent a violation of the Constitution
As to what the president (or anyone) can do about it. It's hard to say. One could argue that congress approved the spending by signing the various bills doing the spending into law, but that doesn't necessarily mean that they approved the borrowing, they could have planned to pay for it some other way. However, since they didn't make any laws to pay for it in another way, one might reasonably assume that they meant for the money to be borrowed, because that's how it works any time we don't run up against the clearly unconstitutional debt ceiling. Ergo, Congress has implicitly approved the borrowing and no one is usurping any legal powers by going ahead and implementing their implied will.
This is all stupid though. We can't enact contradictory laws, and if we do, we implicitly repeal the contradictory bits of the older law. The current contradiction is that in February of 2010, congress passed a law limiting public debt at 14.294 trillion dollars, and since then, has mandated spending and revenue such that public debt must exceed 14.294 trillion dollars sometime in early August. Present law supersedes past law. Problem solved.