Fannie Mae and Freddie Mac may send the Treasury Department enough money in June to extend by a month government operations under the debt ceiling, giving Republicans and Democrats more time to hammer out solutions to the nation’s finances.

The government-controlled mortgage financiers, under revisions last year to their bailout agreements, turn almost all of their profits over to Treasury. They each say they have considered reversing about $90 billion of writedowns of tax credits, which would boost the remittances.

Fannie Mae signaled in its annual report last week that it will realize $58.9 billion of the unusual gains in its first-quarter results, enough to fund Social Security payments for a month, according to Nancy Vanden Houten, of Stone & McCarthy Research Associates. After including Freddie Mac’s potential windfall and the $5 billion to $10 billion of regular income the analyst said they may post, their June payments could about equal the $100 billion by which former Treasury secretary Timothy F. Geithner told Congress in December the U.S. debt grows on average each month.

“It could mean a pretty big chunk of cash for the Treasury at a time they need it,” said Vanden Houten, a senior government policy analyst at Princeton, N.J.-based Stone & McCarthy.

Fannie Mae and Freddie Mac, which were taken into U.S. conservatorships in 2008 and remain off the government’s balance sheet, are weighing writing up “deferred tax assets” after returning to profitability, a development that means they could face the typical tax requirements of corporations.

Fannie Mae’s 2012 net income totaled $17.2 billion, compared with a loss of $16.9 billion in 2011. Freddie Mac earned $11 billion last year, compared with a $5.3 billion loss in 2011. Under August revisions to their rescue agreements meant to reduce the odds that the backstops could be eventually exhausted, the firms send Treasury the amount by which their net worth after each quarter exceeds $3 billion, a threshold that falls to zero over time.

Andrew Wilson, a spokesman for District-based Fannie Mae, and Brad German, a spokesman for McLean-based Freddie Mac, declined to comment, as did Denise Dunckel, a spokeswoman for their overseer, the Federal Housing Finance Agency.

Fannie Mae’s potential big earnings are “an accounting issue between the company, its auditors and its regulator,” Treasury spokesman Anthony Coley said in an e-mail.

President Obama in February signed legislation temporarily suspending the $16.4 trillion debt limit through May 18. Treasury has said that after that date it can use “extraordinary measures” to maintain borrowing ability.

Those steps should give Treasury borrowing room until late August or early September, said Lou Crandall, chief economist at Wrightson ICAP in Jersey City, N.J.

Geithner, who has been replaced by Jack Lew, told lawmakers that “on average, the public debt of the United States is increasing by approximately $100 billion per month, although there are significant variations from month to month.”

The debt of Fannie Mae and Freddie Mac, which the United States has pledged to back without officially guaranteeing, isn’t included in a tally of the U.S. government’s total. The firms, which mainly package mortgages from lenders into securities they guarantee, have drawn $187.5 billion from Treasury since being seized and sent back $65.2 billion in dividends.

Fannie Mae delayed its annual report last month, saying it was a close call whether it should take the step of writing up its deferred tax assets in the quarter ended Dec. 31. When finally making the filing, the company said two issues arguing against the move would no longer be true on March 31.

It will probably no longer have cumulative losses over the previous three years, and taking the step then won’t cause a $34 billion reduction in its remaining Treasury funding line, based on the details of its bailout, according to the filing.

While Vanden Houten said the firms may use asset sales to come up with the money for any unusually large payments tied to the non-cash accounting gains, analysts at Deutsche Bank and FTN Financial say they probably will turn to the debt market, creating additions to their interest costs.

In January, Fannie Mae’s portfolio of liquid investments jumped by almost $28 billion, a sign that it “may already have taken the first step toward raising longer debt for a Treasury payment,” Steven Abrahams, a New York-based Deutsche Bank analyst, wrote in a report last week.

— Bloomberg News