Low deposit rates at Citigroup are "a reflection of the state of competition," said the bank’s finance chief, John Gerspach. The widening gap between loan rates and deposit rates helped drive Citi’s U.S. retail banking revenue up 7 percent, he said.

Asked when banks would start paying more, JPMorgan Chief Financial Officer Marianne Lake said she expected banks to “remain quite disciplined” on rates through the remainder of 2018.

After Bank of America reported results on Wednesday, CFO Paul Donofrio told analysts the bank will eventually have to raise rates on smaller accounts.

"My guess is we are getting close to that point, given the expected fed funds rate hikes," Donofrio said.

Analysts and bankers pointed to recent tax reform as one potential force of change.

Tax Changes Could Spur Higher Rates

Now that corporate tax rates have dropped to 21 percent from 35 percent, there may be stronger demand for loans, which in turn could spark higher rates for deposits to fund them, they said.

And, if the Fed keeps lifting rates in the months ahead, as Wall Street predicts, consumers may start drawing down on deposits, leading banks to use some of their own tax savings to pay more competitive rates.

It is a question of when, not if, said Jefferies’ Usdin.

"We are all waiting for that moment when the retail depositor does have that wake-up moment,” he said, “but I don't feel like it is happening this quarter.”