Are We in a Trap Situation?

The Fed has been pushing back on inflation constantly by saying it's transitory. The fed wants us to believe that inflation is transitory so that they can focus on the unemployment part of their job. And that's going to lead to a head at some point. On the one hand, they want to keep everything easy. They want money to keep flowing. But if that meets headlong into persistent inflation,. And what what t does persistent inflation do for the fed?