WASHINGTON — The nation’s Social Security and Medicare programs are sliding closer to insolvency, the federal government warned in a new report underscoring the fiscal challenges facing the two mammoth retirement programs as baby boomers begin to retire.

Medicare, which will provide health insurance to more than 50 million elderly and disabled Americans this year, is expected to start operating in the red in its largest fund in 2024, according to the annual assessment by the trustees charged with overseeing the programs. That’s unchanged from last year.

And the Social Security trust fund, which will provide assistance to more than 45 million people in 2012, will be unable under current trends to fulfill its obligations in 2033, three years earlier than projected last year.

“We must take steps to keep these programs whole for the future,” Treasury Secretary Timothy F. Geithner, the senior trustee, told reporters Monday.

If the Social Security and Medicare funds were exhausted, they would still be able to pay benefits because they would continue to collect tax revenue. But the deficits would likely force major cuts.

The dismal outlook was fueled in part by the sluggish economy, which has slowed growth in payroll taxes that sustain the trust funds, according to the trustees, who include administration Cabinet secretaries and two public representatives.

That sparked a round of calls from around Washington on Monday for a new effort to tackle the entitlement programs. Most immediately, the trust fund that pays for disability benefits for more than 10 million people is projected to run out of money in four years.

“Leaving Medicare and Social Security on auto pilot and allowing them to continue to grow beyond their means is no longer an option,” said Sen. Orrin G. Hatch of Utah, the senior Republican on the Senate Finance Committee.

Over the last three decades, Republicans and Democrats have periodically forged compromises that extended the solvency of Medicare and Social Security. At one point in the mid-1990s, Medicare’s hospital trust fund was projected to run out of money in four years.

It is unclear whether a similar compromise is possible today. Medicare, in particular, has emerged as a central flash point between the two parties.

Congressional Republicans have twice in the last two years pushed legislation to largely privatize Medicare by giving beneficiaries vouchers to shop for commercial insurance, a plan they say would give seniors more choice and help bring down costs. Former Massachusetts Gov. Mitt Romney, the presumptive GOP presidential nominee, is backing a similar strategy.

Depending on how they are structured, voucher programs — or “premium support,” as proponents call them — can shift thousands of dollars of medical bills onto seniors. The nonpartisan Congressional Budget Office has calculated this is the primary way in which such programs would save the government money.

President Obama and his allies on Capitol Hill have largely resisted this approach, looking instead to the new healthcare law to restrain rising costs in Medicare by forcing medical providers to become more efficient.

This strategy has produced mixed results in the past, as elected leaders sometimes retreat from making politically difficult cuts. This week, the Government Accountability Office questioned the Obama administration’s decision to roll back planned cuts in payments to commercial insurers that administer popular Medicare Advantage plans.

Other cost-cutting steps have been more successful, and growth in Medicare spending per person has slowed in recent years, a major milestone.

But Medicare faces a larger problem as baby boomers retire. The number of beneficiaries is projected to hit 80 million by 2030.

noam.levey@latimes.com