Unless I've missed something, the 14th amendment doesn't even apply here - ratification debate aside. We've got the revenue to address our debt, as well as cuts we can make to address future shortfalls.
14th amendment isn't a non-issue here as the argument isn't over validity of debt, or even the paying of debt - it's an argument over increasing the debt limit so we can go further in debt.
What's happening here, in essence, is that the US's credit card is maxed out. Some politicians, Obama included, want to raise the credit limit and keep spending. Others are (supposedly/now hypocritically/whatever) saying "No, we've got to pay down our balance, instead." Not raising the credit limit does not imply an argument against the validity of the debt, it implies that going even further in debt is simply retarded.
And everyone whines about the cuts, but there's PLENTY of breathing room as far as come to cuts anyway, and we're not even AT the point of default after Aug. 2nd - it's all scare tactics to get the credit limit raised. DOE's obviously on the chopping block as far as I'm concerned (since they've apparently HURT test scores), our intelligence agencies are even more bloated and less efficient at this point (streamline them and cut the fat so they're light and fast - and willing to show results to keep their future funding!)...so many options here.
Regardless, though, it's not even a valid point to bring in the 14th amendment. It says nothing to recognize the validity of future debt some people WANT to accrue.