Welch said it is no surprise how difficult the issue is for members of the Senate, since banks of all sizes are telling members they are worried about new fee limits, while retailers are telling members that high debit-card fees are making it harder to make ends meet.

Welch said he believes the large banks are trying to make the case the fee limits will hurt smaller banks, which he says is incorrect because Dodd-Frank exempts banks with less than $10 billion in assets. Nonetheless, he said, the argument appears to be sticking, thanks in part to what he called an "all out carpet bombing" advertising campaign on the part of the big banks.

"What's difficult about this vote is the big banks have been quite shrewd and effective in using the small banks to make their case," he said. Welch said that even small banks from his home state of Vermont are telling him they are apprehensive about the prospect of new rules that limit fees, which the Federal Reserve is on track to put into place in late July.

Welch generally downplayed the proposal from Sen. Jon TesterJonathan (Jon) TesterBanking panel showcases 2020 Dems Cortez Masto poised to become DSCC chair Mellman: The triumph of partisanship MORE (D-Mont.) to delay the rules for a year, and said Tester and other supporters are essentially trying to permanently derail the rules. "Delay is generally the preferred tactic to derail legislation," he said.

He also agreed with Sen. Dick DurbinRichard (Dick) Joseph DurbinSenate barrels toward showdown over Trump's court picks Overnight Health Care — Presented by The Partnership for Safe Medicines — GOP lawmaker pushes back on Trump drug pricing plan | Pfizer to raise prices on 41 drugs next year | Grassley opts for Finance gavel McConnell: Criminal justice bill unlikely this year MORE (D-Ill.) that banks never want to see the rules put in place because they receive more than $1 billion in debit-card fees each month, which gives them an incentive to delay as long as they can. "It's a candyland for them," he said.