full disclaimer: I am not an expert.
If the interest rate goes up, the Federal budget is fucked
It's always manageable so long as they can borrow more by selling bonds. If they can't sell bonds then yes the country is fucked.
the interest rate doesn’t go up, inflation will runaway and eat the value of the dollar until it is worthless.
It will not "runaway". dollar value will go down initially which would automatically make every product US produces cheaper which will increase exports. Most people would suffer though.