Payday lenders say big banks are denying them service at the behest of federal regulators. The banks, they contend, are threatening to cut them off unless they stop offering payday loans. In one e-mail publicized by Sen. David Vitter (R-La.), a banker cited regulatory action in a decision to deny credit to a payday lender: “Based on your performance, there’s no way we shouldn’t be a credit provider. Our only issue is, and it has always been, the space in which you operate. It is the scrutiny that you, and now that we, are under.” Federal regulators deny compelling banks to sever ties with the lenders, although regulators have told banks that doing business with companies that inflict such harm could damage a bank’s reputation and leave it vulnerable to litigation.