Fraught negotiations in Washington have yielded a deal on raising the U.S.’s borrowing capacity without sending the stock market into a tailspin, as some on Wall Street had feared they might. But more risks may lie ahead.

Investors who spent the better part of the past month fixated on the welter of debt-ceiling related headlines may have missed a major shift in expectations for Federal Reserve monetary policy. Instead of expecting the Federal Reserve to refrain from raising interest rates again in June and deliver multiple…