Firstly, I'd like to point out that I don't necessarily agree. I think it's both a pretty legal argument and politically convenient, so I quite like it. But nobody knows if it's actually true, because obviously, the Supreme Court.
Imagine a budget that said "borrow one hundred dollars and spend it on X". Okay, president is going to go ahead and do that. Then congress says "don't borrow any money". What? That contradicts itself. That's what the debt ceiling does, according to this argument.
The problem with your argument is that the President has nothing to do with spending the money other than to sign the spending legislation. The argument hinged on section 4 of the 14 amendment which reads in part;
"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."
The problem is the next section of the amendment reads, "The Congress shall have the power to enforce, by appropriate legislation, the provisions of this article."
I don't think the Supreme Court rules in the President's favor and gives him the power to override congress and raise the debt ceiling. However you cut it that would give the President to the power to spend money congress did not approve. If congress contradicts itself it is up to congress to sort it out.
But Congress has already approved the spending! In fact, they've made it mandatory! Now they say don't spend that money, without repealing that earlier law. The law contradicts itself.
