No, It Doesn't.

 WaPo letter to the editor headline:

The Constitution demands the debt be paid. Period.

The letter, from one Maurice F. Baggiano, claims:

As long as public debts are authorized by law, they may not be questioned and must be paid. That’s the import of Section 4 of the 14th Amendment.

The 14th Amendment does indeed say that "[t]he 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."

It says nothing whatsoever even hinting at the idea that said debts must be paid, though.

Millions of Americans, and probably billions of people around the world, default on debts every year without "questioning the validity" of those debts. Delinquent mortgages get foreclosed on. Cars get repossessed. Subscriptions get canceled and sent to collection agencies, all with no one ever asserting that the debts weren't valid.

The US government itself, as Alex J Pollock notes at The Hill, has defaulted on its debt no fewer than four times, three of them since the ratification of the 14th Amendment.

Furthermore, there is no requirement, as Baggiano implies, that Congress must pay on existing debt by raising the "debt ceiling" and borrowing even more money. It could just cut spending on other things to leave revenue remaining for debt service.