Raising the eligibility age for Medicare sounds like a fiscal no-brainer.

After all, the Social Security retirement age is rising to 67. It would seem sensible for Medicare to have the same rule.

After all, life expectancy is growing. Today, the average 65-year-old can expect to live another 20 years — about five years longer than when Medicare started.

After all, federal health-care spending is on an unsustainable course. Something’s got to give.

Amid the entitlement mumbo jumbo, raising the eligibility age is attractive to politicians casting about for savings because it is tangible. It is at the top of the Republican wish list. It was part of the never-consummated deal that House Speaker John Boehner and President Obama crafted last year — although House Minority Leader Nancy Pelosi has declared her opposition.

Here’s the wrinkle: This no-brainer turns out to be exceedingly complicated. The savings aren’t as big as you might imagine, because costs to other government health programs would rise as a result. Meanwhile, the move could have an array of problematic effects, from leaving seniors uninsured to raising premium costs for many others.

The Congressional Budget Office (CBO) estimates that gradually increasing the eligibility age to 67 would save $113 billion over the next decade; the savings in the second 10 years, with the cuts fully implemented, would be larger. By 2035, Medicare spending would be 7 percent lower than otherwise expected, or 5 percent when taking into account higher spending on other programs. This isn’t chump change.

The Kaiser Family Foundation, calculating the effect of an immediate change, came up with a much smaller number: less than $6 billion in 2014. Kaiser found that raising the eligibility age would reduce Medicare spending on those seniors by $31 billion that year. But then Medicare premium receipts would drop by $7 billion because some seniors would not be paying into the program. Meanwhile, because some of the newly Medicare-less seniors would turn to the new health-insurance exchanges to obtain insurance, federal spending on the exchanges (premium and cost-sharing subsidies for lower-income seniors) would increase by $9.4 billion.

And federal spending on Medicaid, the health care program for the poor, would increase by $8.3 billion as the poorest seniors enroll in Medicaid under the new expanded-coverage part of the health care law.

Of course, that full Medicaid cost might not materialize if states choose not to participate in the Medicaid expansion, as the Supreme Court has allowed. But then you’d have some poor seniors — by the way, those likely to be in the worst health — left uninsured.

Indeed, the problem of uninsured seniors is a big part of the difference between Kaiser (the organization assumed that everyone would find new coverage) and the CBO, which estimated, before the Supreme Court ruling, that 5 percent of 65- and 66-year-olds would be uninsured. Yes, you can save money on government health programs by kicking people off. Leaving more people uninsured hardly sounds like good policy.

Paradoxically, with the higher eligibility age, the federal government would spend less money, but overall national spending on health care would rise because Medicare costs are lower than those of private insurers.

Meanwhile, with the youngest seniors out of the Medicare system, Kaiser estimated, premiums for the remaining seniors would increase by 3 percent because that population becomes older and sicker. Likewise, premiums on the health-care exchanges would increase by 3 percent, as the average age of enrollees (and therefore the average cost) rises. The risk pools get messed up in both directions.

And many of the newly ineligible seniors, the CBO said, would pay higher premiums or spend more out of pocket. This is not a problem for better-off seniors who’d simply turn to their employers or their retiree health plans; indeed, it would make them more conscious of costs.

But consider the 65-year-old who makes $46,000 a year — too much to qualify for federal insurance subsidies — and whose exchange premiums could reach $12,000. How is this affordable?

Raising the eligibility age would make sense if the neediest seniors are protected. The University of Pennsylvania’s Ezekiel Emanuel has intriguingly proposed tying age limits in Social Security and Medicare to lifetime earnings: the richer you are, the longer you wait to collect benefits. Those with earnings in the bottom half would be shielded from any age increase.

The lesson of health-care reform is that every tweak to this complex mechanism has far-reaching, often unintended, consequences. Raising the eligibility age is worth debating but not without considering the ripple effects of this seemingly simple change.