The Fed delivered a dovish enough message to drive stocks to record highs and bond rates lower, but that tone could change if inflation really does become a problem.
Some traders said they were surprised the Fed did not say more about inflation, after Wednesday's consumer price index showed inflation running at 2.1 percent over last year. Bond yields rose on the inflation data but were lower Wednesday.
"The Fed is deathly afraid of a rise in rates stomping out the recovery. It's clear they will allow inflation to run higher than it should be in order to achieve that," said Peter Boockvar, chief market analyst with Lindsey Group. "What's going to be the end result is the bond market is going to start dictating policy...next week PCE is going to point to that."