Exactly, they are in dilemma. They accept job losses and a cooler economy for a few years or inflation could become a permanent feature of the US economy. Maybe I am wrong but if the FED doesn't find a way to undo their excesses then permanent higher inflation could make the US economy behave more like Latin America economies were high consumer inflation and diminishing purchasing power is a feature.
But unlike Latin America, interest rates going up is even more crippling due to the high debt load, both public and private, which went to asset purchases in some cases but I many was wasted. And they can't default as most of their debt is held by their own citizens as they are so fond of saying.
That's the dilemma: high inflation can eliminate debt, but cripples the consumer -> collapse in spending -> collapse. Reducing inflation with high interest leads to inability to service the debt -> collapse in lending activity and thus economic activity and even higher future interest rates -> collapse.
That's the stagflation hyperinflation trap that happens when you have too much debt and try to inflate it away.