It's unlikely to happen, because the US has a sovereign currency. Inflation is also not a real big concern these days, just the opposite. There's also the fact that if they cause inflation, well the national debt is calculated in US dollars so the real value of the national debt goes down if you inflate the currency. There's no situation where they run out of money and can't pay out bank accounts, if they really want to. And the last thing they want to do is to create any situation where you can't trust bank accounts. They'll inflate the currency to the moon if needed before that happens. The Fed has literally infinite ability to provide funds to banks if needed and they'll take over banks to ensure deposits if all else fails.
This is also why the Republican debt hawks are wrong, or being deliberately obtuse. A balanced budget isn't one with no deficit, it's actually one where the inflation-adjusted debt doesn't increase. So, if inflation was 2%, then you're doing ok if the deficit is < 2% of the outstanding debt. That means in the long run debt is decreasing in real-value terms. If debt was $20 trillion and inflation 2% then a $400 billion deficit is actually the break-even point on that.
If they have no deficit they'd probably crash the entire economy. That's not worth it when inflation deals with long-term debt for you without having to destroy everything in the short term. The way they're pulling the wool over your eyes here is they're deliberately conflating real value with adjusted value. If the gold standard existed*, then the balanced budget argument would make sense: if you have a deficit then the actual value of the debt is increasing each year. However, there is no gold standard and the value of a dollar next year is less than the value of a dollar this year, so to work out whether you're getting richer or poorer, or more in debt vs less in debt, you do need to factor inflation in. Which they definitely know but are hoping you don't know.
* And don't even get started on that "bring back the gold standard" bullshit. The argument for returning to the gold standard is like saying that because your car has steering issues, you nail the accelerator pedal in place so that it's only got one setting.