you'd get a bigger tax bill.

Not necessarily. I don't think USA has to cut a check to cancel these, I think they just have to stop asking for repayment.

I think you’re right that they just have to stop asking for payment but I assume those payments were included in the budget. The shortfall will need to be made up somewhere. Either higher taxes or fewer services.

Maybe the government should do this all the time. Housing crisis? Medical bill crisis? No problem, just have the federal government "loan" them money, then don't ask for repayment!

There is no difference in practice. Government spending is not going to change, but the amount coming in will decrease. That means either increased taxes or increased government debt.