When the Federal Reserve raised benchmark interest rates last month, it took North Carolina lender BB&T Corp. less than an hour to announce it was passing that cost along to borrowers. Depositors, however, have yet to see the benefit.

For many investors, such discipline means U.S. banks are about to feast on rising interest rates — profiting from a fatter margin between what they charge for loans and the rewards they offer depositors who provide the funds. Now, a small but growing chorus of senior executives and analysts is signaling that resolve may fray and that shareholder optimism is too high.

Banks are under unprecedented pressure to break ranks and compete for deposits. Compared with past cycles, more savers are web-savvy — able to comparison shop and transfer money online to firms offering better deals. Money-market funds that suffered for years with near-zero rates are eager to lure back customers. And new liquidity rules encourage banks to draw more funding from consumer deposits, pushing lenders to fight for those clients.