Daniel Tarullo, governor of the U.S. Federal Reserve, listens during a Senate Banking hearing on derivatives regulatory framework in Washington, D.C., U.S., on Tuesday, April 12, 2011. (Andrew Harrer/Bloomberg)

One of the most influential policymakers at the Federal Reserve, Daniel Tarullo, publicly debated options Tuesday for ending bailouts of big banks considered too big to fail, signaling that the contentious issue may move to the forefront in the coming year.

The proposals attempt to limit the risks the nation’s largest banks can pose to the financial system, and ultimately taxpayers, if they collapse. Policymakers have been emboldened by public outrage over the continued growth of megabanks.

Critics also note that although the program that bailed out the nation’s banks during the 2008 financial crisis has all but ended, the ensuing Dodd-Frank financial reform law did not definitively ban the government from future bailouts.

The strategies for mitigating the risk these massive firms pose to the financial system span the ideological spectrum, from regulators who want to break up large banks outright to lawmakers pressing for caps on their activities.

In a speech at the Brookings Institution on Tuesday, Tarullo, the head of bank supervision at the Fed, stopped short of calling for permanently abolishing government backstops for banks. But he laid out policies to contain the problem, some of which would require fresh legislation.

“The policy aim has got to be to confine the problemsubstantially more than it was in the years running up to the crisis,” he said. “That seems to inexorably call for a set of complementary policy measures” to Dodd-Frank.

Provisions in Dodd-Frank — including orderly liquidation and requirements to keep more money in reserves — limit safety nets or place restrictions on large bank activity. Implementation of these statutes has been slow going as regulators and bankers battle over the fine points.

Tarullo said strides have been made toward enacting many provisions, but he encouraged additional steps to address the complexities of reform.

One such step would be requiring large financial firms to set aside more money that could be tapped in the event of its failure. The Federal Deposit Insurance Corp. and the Fed are in discussions to flesh out this proposal, according to people close to the matter who were not authorized to speak publicly.

Regulators can do this without additional legislation because of new powers granted through Dodd-Frank.

Tarullo said the new capital requirement could lend greater confidence that investors and creditors, not taxpayers, would bear all losses at a failed bank. Most banks are healthy enough to meet this standard, though they may face additional costs.

Tarullo also reiterated an idea that he has been pitching for months: restricting the expansion of big banks by limiting their non-deposit liabilities — funding that comes from sources other than consumer deposits in savings or other accounts. The plan targets behemoths such as ­JPMorgan Chase and Citigroup who rely heavily on such funds, Tarullo said, which makes banks more vulnerable in crises.

Tarullo has yet to offer details on the size of the cap but is calling for more analysis of the potential impact of the proposal.

The Fed governor is the highest-­ranking regulatory official to call for capping the size of banks in some fashion, but not the only one. Thomas Hoenig, vice chairman of the FDIC, is promoting a plan to break up the largest banks by separating their traditional commercial banking divisions from their riskier investment activities.

“Right now, if you’re a broker dealer and you don’t have a commercial bank, you’re at a competitive disadvantage because you don’t have a safety net. It’s driving them out or into a bank, and that’s consolidation, concentration that we don’t need,” Hoenig said in an interview.

Lawmakers, including Sen. Sherrod Brown (D-Ohio), introduced legislation addressing bank size during the Dodd-Frank debates that failed to garner enough support. Since then, the tenor of the debate has changed.

With liberals such as Elizabeth Warren entering the Senate and too-big-too-fail opponent Rep. Jeb Hensarling (R-Tex.) taking the helm of the House Financial Services Committee, some analysts say the issue is likely to resurface in 2013.

Industry watchers remain skeptical about lawmakers’ proposals to break up big banks, but some are encouraged by Tarullo’s call for more analysis.

“To the extent that Tarullo takes a leadership role in getting the evidence to back up any conclusions is much more productive than just having members of Congress introduce legislation or create dynamics that force regulators to do things without merit,” a representative from the financial industry said.