That figure would be nearly twice the amount Fannie and Freddie have received so far. To date, the rescue of the two companies has cost taxpayers $135 billion. They have repaid $13 billion to the Treasury Department as dividends.
By contrast, the combined bailouts of financial companies and the auto industry have cost taxpayers roughly $50 billion, according to Treasury's latest projections. And the bailouts of Wall Street banks alone, which sparked public fury, have so far brought taxpayers a $16 billion return.
Fannie and Freddie were battered by losses on loans they backed, once the housing bubble burst and foreclosures soared. The two companies buy home loans from lenders, package them into bonds with a guarantee against default and sell them to investors.
On Thursday, the government provided a broad estimate of the costs of bailing out Fannie and Freddie. The final cost will depend on the direction of home values over the next few years. If prices fall sharply, as some analysts forecast, Fannie and Freddie won't be able to recover as much money on foreclosures. They would require more taxpayer aid.
The Fannie-Freddie bailout could end up costing taxpayers between $142 billion and $259 billion through 2013, the Federal Housing Finance Agency projected. The worst-case scenario assumes the economy would fall back into a recession and home prices would sink an additional 24 percent, until early 2012.
The best-case scenario assumes home prices remain flat for the next two years.
"If the economy does unravel in the next couple of quarters, then the costs will mount very rapidly," said Mark Zandi, chief economist at Moody's Analytics.
Thursday's estimate was the first time the housing agency has released a public estimate of the taxpayer tab. The combined bailout of the two mortgage companies is on track to be the largest of the financial crisis.
The agency's figures take into account dividends that the agency estimates Fannie and Freddie will end up repaying. The terms of their rescue require them to pay a 10 percent annual dividend to Treasury. That amount is expected to balloon in coming years. Regulators expect Fannie and Freddie to repay an additional $67 billion to $91 billion in dividends over the next three years.
The two mortgage finance companies have been operating under federal control for more than two years. When the government stepped in to take them over in September 2008, their rescue was expected to cost only a combined $200 billion.
Allegations that mortgage lenders nationwide cut corners on foreclosure documents as they moved to seize millions of homes have put Fannie and Freddie under scrutiny. The two companies have used so-called "foreclosure mill" law firms that are accused of processing thousands of files in haste.
A deposition released by the Florida attorney general's office this week revealed that the office manager of the Florida-based Law Offices of David J. Stern, which Fannie and Freddie used, would sign 1,000 files a day without reviewing them. The deposition also said the office manager allowed paralegals to sign her name when she got tired.
Fannie and Freddie say they're suspending use of that firm.
Several banks have been accused of similar conduct. If they can't resolve their foreclosure problems and are barred from seizing many homes, Fannie and Freddie could absorb huge losses on loans they own or guarantee. That's because they would no longer be able to recover anything on loans that have gone bad.
Delays in foreclosures would hurt Fannie and Freddie in areas of the country where home prices are falling. The longer they wait to sell homes, the less money they stand to recover.
But some analysts doubt the document mess will have much impact on Fannie, Freddie or the pace of foreclosures. It's likely to result in weeks of delays for foreclosures, not months, Zandi said.
Fannie and Freddie own or guarantee about half of all U.S. mortgages, or nearly 31 million home loans worth more than $5 trillion.
The bill for rescuing Fannie and Freddie has been rising, while the estimates for other rescues have been sinking. What was once the most expensive single bailout American International Group Inc. is now projected to cost taxpayers only $5 billion.
Even that bailout could turn a profit, Treasury said this month, depending on the price it gets on its future sale of AIG shares. The Obama administration's rescue of the U.S. auto industry is projected to cost $17 billion, Treasury has said.
Over the next year, lawmakers plan to review the nation's mortgage-lending system and consider a potential replacement for Fannie and Freddie. The financial overhaul law didn't address that issue.
Republicans have blasted the Obama administration's handling of Fannie and Freddie, saying the government's reliance on them to modify home loans for troubled borrowers is increasing the cost of their bailout.
"At some point, we have to say, enough is enough, and push forward with a complete overhaul of the government-backed mortgage giants," said Rep. Scott Garrett, R.-N.J.
He said the ballooning costs of their rescue highlight the need to replace Fannie and Freddie with a new system of providing mortgages.
AP Business Writers Christopher S. Rugaber and Daniel Wagner contributed to this report