Some lawmakers are saying it’s time to look again at breaking up the country’s biggest banks, but political observers say the odds of action just two years after overhauling the financial regulatory system are remote.

“I don’t think that Congress is going to step into this,” said Brian Gardner, a banking industry analyst with Keefe, Bruyette & Woods. “I think they had their shot. I think it’s tougher to go back and do it again.”

Criticism of the idea that some large financial institutions are still “too big to fail” has persisted across the political spectrum, and Daniel K. Tarullo, a governor of the Federal Reserve, bolstered that view in a speech this month saying that Congress should set new boundaries on the growth of large banks.

In a speech Oct. 10 at the University of Pennsylvania Law School, Tarullo suggested that an “upper bound” for financial firms could be set through limiting their non-deposit liabilities to a percentage of U.S. gross domestic product.

Tarullo said a gap in regulation means large banks are not constrained by the kind of anti-monopoly provisions that the Sherman Act places on other industries. “It means that the current structure for financial stability regulation permits substantial increases in systemic risk, so long as it is generated from internal growth,” he said. “To the extent that a growing systemic footprint increases perceptions of at least some residual too-big-to-fail quality in such a firm, notwithstanding the panoply of measures in Dodd-Frank and our regulations, there may be funding advantages for the firm, which reinforces the impulse to grow.”

“It would be most appropriate for Congress to legislate on the subject,” Tarullo added.

He left many details to be determined, but the comments showed there is support for a new look at banking regulation four years after the financial system was brought to the brink of collapse, and two years after the Dodd-Frank law (PL 111-203) was enacted in hope of preventing similar financial crises and federal bailouts.

“This is a debate well worth having,” Tarullo said.

But legislative action would be needed to impose a cap on the size of banks, and observers say there is no appetite among lawmakers for doing so.

When writing the 2010 regulatory overhaul, lawmakers, the Obama administration and federal regulators considered forcing banks to downsize but decided against it.

Senate Democrats Sherrod Brown of Ohio and Ted Kaufman of Delaware pushed an amendment to the bill that would have limited bank holding companies’ non-deposit liabilities to 2 percent of GDP. It was rejected 33-61. Brown has introduced legislation (S 3048) with similar provisions, but the bill has not seen action and is unlikely to advance.

Still, concern about “too big to fail” remains potent in both parties.

This week, the top Democrat and Republican on the House Financial Services Committee released rival white papers arguing over whether the Dodd-Frank law prohibits future bank bailouts. And support for targeting large financial institutions has created a coalition of strange bedfellows. In August, Brown, a liberal stalwart, wrote a letter with conservative Sen. David Vitter, R-La., to the Fed encouraging higher capital standards for the biggest banks.

Brown and Vitter followed up with a new letter to banking regulators Wednesday again urging “simpler, more robust capital rules.”

Thomas Hoenig, a member of the Federal Deposit Insurance Corporation whose nomination was offered by Senate Republicans, has been a vocal supporter of breaking up large financial institutions, and Richard Fisher, president of the Dallas Fed, has made similar comments. Former Citigroup CEO Sanford Weill, the godfather of the behemoth financial institution, shocked the financial world when he declared in July that some large firms should be split up.

Mark A. Calabria, director of financial regulation studies at the libertarian Cato Institute and a former Senate aide, does not expect Congress to take up the issue in a serious way, saying wrangling over implementation of the 2010 law was more likely to occupy lawmakers’ focus.

“It’s hard for me to see how this happens in an environment where you don’t sort of repeal and replace Dodd-Frank,” Calabria said, adding it remains unlikely no matter who takes power after the November elections.

“Because there are so many rulemakings and so much controversy around Dodd-Frank, it sort of sucks the oxygen out of the room,” he said.