Any truth to “they can only raise interest rates so much or they won’t be able to service the debt”

I see macro-economists in the media say this all the time. They say that the amount of interest rate hikes needed to aggressively combat inflation is impossible because the Fed and most central banks are pinned to a corner. If they raise interest rates too high, the government will be unable to service the debt.

I know they don't just have to raise interest rates, they can do QT too but is it as simplistic as the argument above which macro-economists make saying that it's impossible to raise interest rates beyond a certain amount?