WASHINGTON — The fight for the Republican presidential nomination sometimes seems to be a contest over who can say the most alarming things about Social Security.

Texas Gov. Rick Perry calls the program a “monstrous lie,” while former Massachusetts governor Mitt Romney, warns of its “looming bankruptcy.” Rep. Ron Paul of Texas says Social Security is “on its last legs.”

The air of crisis is striking, given that the program — far from being broke — can pay promised benefits for the next 25 years. After that, even without fixes such as higher payroll taxes or further increases in the retirement age, it could meet about three-quarters of its obligations through 2085, the latest report of the Social Security and Medicare Trustees shows.

“It’s more of a long-term problem,” said Jim O’Sullivan, chief economist for MF Global Inc. in New York. “Over the long haul, total outlays will start to exceed total revenues, but that doesn’t happen for several decades.”

While portraying Social Security as doomed, none of the Republicans have offered specific proposals to fix the problem. They aren’t alone. After indicating during this summer’s debt-ceiling talks a willingness to curb future cost-of-living increases for Social Security recipients, President Barack Obama exempted the program, which spent $712.6 billion last year, from his deficit-reduction plan unveiled Monday.

“Both parties have seemed to pull back from sensible reforms,” said Maya MacGuineas, president of the nonpartisan Committee for a Responsible Federal Budget.

The two parties’ caution is no surprise. While younger Americans increasingly see Social Security as a bad deal, some of the tax increases and benefit reductions required to repair the program are unpopular. By a margin of 63 percent to 29 percent, respondents in the latest Bloomberg National Poll opposed cutting benefits by changing the formula used to calculate annual cost-of-living adjustments.

The two leading Republican candidates are staking out rival positions, with Perry vowing to “transform” Social Security and Romney casting himself as a defender of the program. Both have been mute on details, beyond promising that current retirees would be unaffected by any changes.

Andrea Saul, a Romney campaign spokeswoman, said the candidate addressed potential Social Security fixes in his book, “No Apology,” and in his jobs plan. In them, he ruled out higher taxes and described an increase in the retirement age, a cut in benefits and individual accounts as “options” without endorsing any single action.

Perry, who drew criticism for labeling the program a “Ponzi scheme,” has praised the example of Galveston County, Texas, where public-sector workers withdrew from Social Security in 1981 and set up a program of individual accounts. Such withdrawals are no longer permitted.

In Galveston, higher-income employees and those with fewer dependents did better than they would have with Social Security, according to analyses by the Government Accountability Office and the Social Security Administration. Workers can’t take benefits with them if they change jobs and payments aren’t indexed for inflation, unlike Social Security.

Catherine Frazier, a Perry spokeswoman, said the governor sees Social Security as “a prime example of what is broken in Washington” and had cited Galveston to show “there are alternatives we should be looking at.”

Perry is one of at least four Republican hopefuls who have lauded individual accounts, like those proposed by President George W. Bush in 2005, as an alternative to traditional Social Security for younger workers.

Allowing workers to divert a portion of their Social Security contributions to a menu of stock and bond index funds offers the chance to accumulate larger retirement savings. Individual account holders, however, would risk outliving their savings, unlike Social Security’s lifetime guarantee.

“You know you’ll have more money at the end of your lifetime if you control it than the politicians,” former House Speaker Newt Gingrich, who’s seeking the Republican presidential nomination, said during a Sept. 12 debate in Tampa, Fla.

By themselves, such accounts would do nothing to buttress Social Security’s financial health. Moving toward such a system would even make the federal budget deficit bigger.

During the shift, Social Security would still be paying benefits to people who retired under the traditional system while some of the incoming payroll-tax revenue would be diverted to the new investment accounts. The government would need to borrow the difference.

“That’s why it’s never going to happen,” said Andrew Biggs, a former White House official who worked on the Bush plan. “Nobody wants to pay the transition costs.”

Biggs, now a resident scholar at the American Enterprise Institute in Washington, said the annual addition to the deficit could be almost $60 billion.

Still, financing arrangements for both Social Security and the Medicare health-insurance program for the elderly “are not sustainable,” the program trustees said, adding that the sooner officials act, the easier the adjustment will be.

Social Security is under stress because people are living longer and there are fewer workers supporting each retiree.

A 65-year-old man in 1940 could anticipate living about 12 more years compared with more than 17 in 2010, according to the May 13 trustees report.

In 1945, the earliest program data available, there were almost 42 workers supporting each beneficiary. That number fell as people began retiring, reaching fewer than three last year.

Fixing the program is easier mathematically than politically. Various combinations of higher taxes, reduced benefits or later retirement ages would suffice. Immediately increasing the combined 12.4 percent payroll tax by 2.15 percentage points or cutting benefits by 13.8 percent would make Social Security solvent for 75 years, the trustees said.

The political storm over Perry’s charge that Social Security is a Ponzi scheme obscured genuine anger among some voters over the program’s generational unfairness.

A Census Bureau report last week found that the only group of Americans not suffering increased poverty is those at least 65 years old. Younger workers now paying the benefits for today’s retirees will earn a much lower return on their Social Security contributions than did their elders.

The first retirees, those born before 1901, earned an 18.4 percent return; those retiring this year received 2.5 percent, according to an analysis by Dean Leimer of the Social Security Administration. Ida May Fuller, the first Social Security recipient, paid $22 in taxes into the program and received benefits worth about $20,000, according to a 1996 paper by Jagadeesh Gokhale and Kevin Lansing, economists with the Federal Reserve Bank of Cleveland.

That generational grievance may explain the public divide over Perry’s Ponzi remarks. The Bloomberg National Poll showed that 46 percent agreed with the Texas governor, compared with 50 percent who disagreed.

Social Security benefits are paid from a “trust fund,” an accounting mechanism that keeps tabs on promises the government has made to pay future benefits. The program is funded by payroll taxes paid by workers and employers on incomes up to $106,800; income earned on Treasury securities; and taxes that higher-income retirees pay on their Social Security benefits.

By law, Social Security is required to invest any surplus funds in special-issue securities guaranteed by the government. That’s how the trust fund ended up with securities, which some program skeptics deride as “IOUs,” rather than cash or some other asset.

Last year, for the first time since 1983, the program’s expenses exceeded its non-interest income. Social Security covered the $49 billion deficit by drawing down its trust fund balance, which it will also do this year.

The fund — worth $2.6 trillion at the end of 2010 — is expected to grow for the next 11 years thanks to interest earned on the securities. After 2022, Social Security will be cashing in so many securities that the fund will begin shrinking until it’s exhausted in 2036, according to the trustees’ report.

The government will need to borrow more, raise other taxes or cut other spending to pay the Social Security Administration for the securities it redeems.

“The bonds in the trust funds will be honored under any reform plan and under any scenario, but we will still have to ultimately figure out how to balance incoming taxes and outgoing benefits,” Charles Blahous, a trustee, said in an email.

There’s no shortage of proposals to extend the program’s lifespan.

All potential solutions involve hard choices.

“I can’t imagine that Congress will sit on its hands and let everyone get a 25 percent benefit cut,” said Peter Diamond, a Nobel Prize winning economist at the Massachusetts Institute of Technology. “The real question with Social Security is not will we fix it, but when?”