On the other hand, if the economy continues to recover, the troubled mortgage companies could require as little as $6 billion in additional aid, the Federal Housing Finance Administration said Thursday.

The Treasury Department has pumped $148 billion into the two companies since they were seized by the government in 2008, to cover their losses on soured mortgage loans. The government is propping up the companies to make sure that money remains available for new home mortgage loans. In return, the companies have paid dividends to the federal government totaling $13 billion, making the net cost to the Treasury $135 billion so far.

The new projections suggest that the companies will not need much more money, so long as the economy does not falter. The housing finance administration, which oversees Fannie and Freddie, said that it was publishing the numbers to inform public debate about the future of the two companies. The Obama administration plans to propose changes to the government?s role in housing finance early next year.

?These projections are intended to give policy makers and the public useful snapshots of potential outcomes for the taxpayer support of Fannie Mae and Freddie Mac,? said Edward J. DeMarco, the agency?s director.

The projections offer three situations. In the most dire, the economy starts shrinking again, driving down prices and increasing defaults. The companies could then require another $215 billion from Treasury. But in this situation they would return $104 billion to Treasury in the form of dividend payments in return for the aid, including the $13 billion already paid to the government. The total cost to taxpayers: $259 billion, including the $148 billion given to the companies since 2008.

In its most optimistic assumption, the agency projected that housing prices would merely stay flat over the next three years. The companies would then require $73 billion in additional aid, and return $67 billion in new dividend payments in addition to the $13 billion already paid. The total cost to taxpayers: $141 billion.

The intermediate assumption is the agency?s best guess about what the future holds. Housing prices would fall a little farther, and then begin to recover. Fannie and Freddie would take about $90 billion in additional aid and return about $71 billion in new dividend payments on top of the $13 billion already paid. The total cost to taxpayers: $154 billion.