The Obama administration has repeatedly boasted how the historic rescue of Wall Street will cost taxpayers far less than originally expected. But the budget proposal released Monday came with some unwelcome news: The price tag of the bailout is suddenly going up.

As a result, the administration said it will seek twice as much money from its proposed bank tax compared with last year, $61 billion vs. $30 billion.

A main reason for the increased bailout cost is that the government’s stock holdings of companies rescued by taxpayers have fallen in value. Insurance giant American International Group’s stock has fallen 36 percent in the past year while General Motors’s has tumbled 30 percent.

In 2011, the administration put the cost of the government’s financial rescue at $28 billion. Now, it’s expected to reach $54 billion.

The proposed “Financial Crisis Responsibility Fee,” which would charge big banks $61 billion over 10 years, would square with President Obama’s political strategy to harness the anger against Wall Street in his reelection campaign. It also would cover the cost of one of his ideas to boost the economy, a program to refinance mortgages for struggling homeowners.

Republicans pledged to oppose the tax, which has never been passed by Congress. But Obama’s team may see political advantage in its proposal, especially if Mitt Romney, with his background in private equity, winds up being the Republican nominee.

The tax would apply to J.P. Morgan, Goldman Sachs and other banks with more than $50 billion in assets, even though these firms have generally repaid their bailouts to the Treasury with interest. Taxpayers may lose far more money in companies, such as the automakers, which won’t have to pay the fee.

“Despite claims to the contrary, the facts on [the federal rescue] are very clear: Taxpayers have profited $13 billion from their investments in banks through the program and Treasury predicts they will see a lifetime positive return of more than $20 billion,” Frank Keating, president and chief executive of the American Bankers Association, said Monday.

He added, “This would simply be an arbitrary tax with no regard to where losses actually occurred.”

The bailout’s costs continue to shift. Shares of AIG and GM, for instance, are above what they were at the end of November, when the budget was tabulated. That means the rescue program is slightly less expensive than the budget suggests.

What’s more, the bailout also sets aside $46 billion for programs to help homeowners. But only $3.3 billion has gone out the door for this purpose, and it is difficult to know how much will ultimately be spent.

The bright spot of the financial rescue is the program to aid banks, the core of which was called the Troubled Assets Relief Program, or TARP. The administration’s budget said the Treasury had reclaimed $258 billion from the banking sector at the end of last year, $13 billion more than was handed out.

Administration officials note that, under the law that created TARP, they are required to recoup the costs of the financial bailout from the financial industry. The bank tax first appeared in Obama’s 2011 budget and was projected to raise $90 billion in 10 years.

The administration’s 2013 budget argues that the tax is justified because many of these companies “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.”

Officials say that the proposed tax would also discourage excessive risk-taking, a cause of the 2008 financial crisis. The tax would equal up to 0.17 percent of a financial firm’s assets.

The costliest part of the government’s rescue during the financial crisis was the bailout of mortgage financiers Fannie Mae and Freddie Mac. The new fee doesn’t encompass that cost.

The Obama budget projects Fannie and Freddie will receive $221 billion in total investments from the Treasury between 2009 and 2013 and pay dividends of $73 billion in exchange over the same period.

The administration sees Fannie and Freddie making enough in 2013 to begin repaying their investments. By 2022, the administration estimates that the cost of the bailout of Fannie and Freddie will be $28 billion, but it added that it does not expect the companies to be around that long.