The US can't practically run out of cash as long as the world reserve currency is the USD. They can print money to pay their debts even to foreign countries. Of course that's a single use get-out-of-jail card. Because once they do that, the USD will cease to be the reserve currency.
Possibly at that point some "other" currency that is not controlled by any single government... perhaps something decentralized.
The government prints a lot already. Although it may be considered a solution, it's also going to make inflation rise as it is happening already in US.
There had been debates about raising the debt ceiling but no one will really want to be portrayed as a bad guy which is likely either Dem or Rep will support it. But we'll see if this someone out there going to stand up and be the one.