The Obama administration on Monday more than doubled to $61 billion a proposed fee it wants the largest U.S. banks to pay for their role in the financial crisis.

Banks with assets of $50 billion or more, or 32 institutions, would be responsible for paying the fee over the course of 10 years starting next year.

The fee, according to further details released by the Treasury Department, would be based on the covered liabilities of the firm, which means a bank's consolidated risk-weighted assets minus its capital insured deposits and certain loans to small business. Treasury said it would charge firms 17 basis points but provide a 50% discount to apply to more stable sources of funding, including long-term liabilities.

"The structure of the fee would be consistent with principles agreed to by the G-20 Leaders and similar to fees proposed by other countries," according to documents in the president's fiscal 2013 budget.

The fee would partly go to offset the administration's new massive mortgage refinancing plan — as initially announced during the president's third State of the Union address last month.

But it's unclear exactly how much of the multi-billion fee, if approved by Congress, would be used to pay for the new program. The administration hopes to reach millions of responsible homeowners, who meet certain eligibility requirements, to enable them to tap historically low interest rates by streamlining the refinancing process.

"While there are signs that the broader housing market is beginning to stabilize, too many Americans are still paying mortgage interest rates far above current market rates because home price declines made them ineligible for refinancing," according to budget documents.

The White House has already said it expects the government's share of the program, which will be overseen by the Federal Housing Administration, to cost anywhere between $5 billion to $10 billion.

The administration, which has sought to take a strong stand against Wall Street firms, has justified asking the largest U.S. institutions to chip in given the risks they took in sparking the crisis.

"Many of the largest financial firms contributed to the financial crisis through the risks they took, and all of the largest firms benefited enormously from the extraordinary actions taken to stabilize the financial system," according to budget documents.

But bankers are already fiercely opposing the fee, noting that the government made money off its investments in banks through the Troubled Asset Relief Program (TARP).

According to the Obama administration's budget, a total of $245 billion in TARP funds was invested in banking institutions. By the end of 2011, the government had recovered $258 billion from those institutions through repayments, interest, dividends and other income.

"So we found that somewhat astounding," said James Ballentine, chief lobbyist for the American Bankers Association, referring to the administration's rationale for the bank tax proposal, "and certainly would be opposed to such efforts."

The fee, which would require legislation and had already been criticized by Republicans even before details were released by the White House, is more than the $30 billion 'bank tax' the administration called for in its last fiscal budget, a measure that failed last year.

Republicans have said any housing plan by the president would be "dead on arrival," if it comes with a fee on the banks.

"It is the idea that just won't go away," Jaret Seiberg, a senior policy analyst for Guggenheim Partners' Washington Research Group wrote in a research note. "The administration has floated the bank tax many times before. It could have gotten it enacted in 2009, but the lift gets harder for each additional year that passes since the height of the crisis."

Separately, the administration reiterated several of its housing policy goals, including evaluating "long-term housing finance reform" and said it has already taken "meaningful steps" to reduce the role of the government-sponsored enterprises.

Earlier this month, Treasury Secretary Tim Geithner announced the White House's intent to outline more specific plans in the coming months to reform Fannie Mae and Freddie Mac. One year has already passed since the administration put forth a paper to Congress outlining three options for a future housing system.

The budget also highlighted efforts by the Federal Housing Finance Agency to develop a pilot program to convert foreclosed homes into rental properties, as well as reforms it made last fall to upgrade its Home Affordable Modification Program in order to provide greater access to borrowers who want to refinance their homes.

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