But what sounds like a prudent sacrifice for an aging society that must watch its budget could have some surprising consequences, including higher premiums for people on Medicare.

Unlike tax hikes, which spawn hard partisan divisions, increasing the Medicare age could help ease a budget compromise because President Barack Obama has previously been willing to consider it. A worried AARP, the seniors’ lobby, is already running ads knocking down the idea as a quick fix that would cause long-term problems. House Democratic Leader Nancy Pelosi, D-Calif., doesn’t like it either.

But for Republicans seeking more than just tweaks to benefit programs, raising the current eligibility age of 65 has become a top priority, a symbol of their drive to rein in government. If Obama and the GOP can’t agree soon on a budget outline, it may trigger tax increases and spending cuts that would threaten a fragile economic recovery.

Increasing the eligibility age to 67 would reduce Medicare spending by about 5 percent annually, compounding into hundreds of billions of dollars over time. But things aren’t that simple.

“This is a policy change that seems straightforward, but has surprising ripple effects,” said Tricia Neuman, a leading Medicare expert with the nonpartisan Kaiser Family Foundation. “It’s a simple thing to describe, and the justification is that people are living longer, but I don’t think people have thought through the indirect effects.”

Among the cost shifts identified in a Kaiser study:

—Higher monthly premiums for seniors on Medicare. Their costs would go up because keeping younger, healthier 65- and 66-year-olds out of Medicare’s insurance pool would raise costs for the rest. The increase would be about 3 percent when the higher eligibility age is fully phased in.

—Higher premiums for private coverage under Obama’s health overhaul. That’s because older adults would stick with private insurance for two extra years before moving into Medicare. Compared with younger adults, they are more expensive to insure.

—An increase in employer costs because older workers would try to stay on company insurance plans.

—Higher out-of-pocket health care costs for two out of three older adults whose entry into Medicare would be delayed.

The Congressional Budget Office has also projected an increase in the number of uninsured. That possibility becomes more real with populous states like Texas saying they won’t accept the Medicaid expansion in Obama’s health overhaul, which would provide coverage to low-income adults. Then there’s the impact on people with physically demanding jobs, for whom extending their working years may be difficult.

Still, the idea isn’t going away.

Polls show that many Americans are willing to consider raising the age at which people become eligible forMedicare benefits as part of a plan to reduce deficits, even if on the whole it’s still unpopular.

A new Associated Press-GfK poll found that four in 10 back gradually raising the eligibility age, while 48 percent oppose that plan.

Those under age 30 were most supportive, while a clear majority of those between the ages of 30 and 64 were opposed. Seniors were split. Surprisingly, there were no significant differences by political party. Overall, foes of the idea were more adamant, with strong opponents outnumbering strong supporters by 2-1.

U.S. life expectancy has risen by about eight years since Medicare was created in 1965. During the 1980s, Republican President Ronald Reagan and Democratic congressional leaders agreed to gradually increase the age for receiving full Social Security benefits from 65 to 67. But they didn’t touch Medicare eligibility.

Since then, some policy experts have advocated aligning the Medicare and Social Security eligibility ages through a gradual phase-in that would spare those close to retirement.

The idea gained new life when Republicans won the House in 2010, and Budget Chairman Paul Ryan, R-Wis., embraced it. Obama indicated he was open to it during budget talks with Republicans in 2011. But the president quickly retreated, and now says he’s not willing to consider cutting Medicare unless Congress agrees to raise taxes on the wealthy.

The No. 2 Democrat in the House, Maryland Rep. Steny Hoyer, says raising the eligibility age and other cuts “clearly are on the table,” although he doesn’t see much chance for them if Republicans don’t yield on taxes.

For his part, House Speaker John Boehner, R-Ohio, has relented from pursuing other major changes toMedicare, such as privatization. But when it comes to the eligibility age, he is still pushing.

“It’s a structural change but it doesn’t require you to adopt a whole new model,” said Scott Gottlieb, a health policy expert with the business-oriented American Enterprise Institute. “It can be enacted quickly so you get the savings, and it can be phased in so you don’t affect people about to retire.”

AARP and other groups representing older adults are mobilizing against it.

“We are prepared to oppose this one pretty strongly,” said AARP legislative policy director David Certner. “It’s a pretty big deal.”