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 TesterJon TesterOvernight Defense: Pentagon chief urges Congress to approve budget boost | Senate fight over NATO addition Defense chief after Trump tweet: NATO doesn't track 'past money owed' Eye on 2018: Five special elections worth watching 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 DurbinDick DurbinGorsuch rewrites playbook for confirmation hearings Gorsuch: I'm 'sorry' for ruling against autistic student Mattis on defense budget boost: 'America can afford survival' 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.