Trimming the federal budget deficit by raising the eligibility age for Medicare from 65 to 67 meets H.L. Mencken’s definition of an answer to a complex problem that is “clear, simple and wrong.”

The argument in favor of this much-discussed idea is that Medicare is one of the big-ticket entitlements that need to be “reformed” to prevent the country from sliding off the fiscal cliff, a draconian combination of tax hikes and spending cuts that could push the economy back into recession. Americans are living longer than they were when Medicare was created in the 1960s, and so pushing eligibility off for two years will help ease the actuarial pressure of the baby boom generation’s march to retirement.

But cutting people off Medicare won’t make their health needs go away, and people will still need health insurance when they reach age 65. Some will be able to afford it on the individual market; others will be able to get it through their employers. Some will be covered by state Medicaid programs, and some will be eligible for government-subsidized coverage under the Affordable Care Act. But many, perhaps hundreds of thousands of Americans, according to a recent study, will have no health insurance, rely on charity care from hospitals and – if they live – enter the Medicare system sicker at 67 than they would have been if they came in at 65.

So, the savings realized by raising the Medicare eligibility age could just show up as liabilities in the budgets of state and federal programs as well as private insurance premiums.

When you look at the Medicare population, people ages 65 and 66 are the youngest, healthiest and cheapest to cover with health insurance, and putting more of those people in the pool shares the costs more affordably.

Rather than cutting people off Medicare or cutting covered benefits, Congress should focus on ways to reduce health care costs overall, which will make government insurance less expensive. Programs that cut costs by rewarding providers who avoid mistakes and keep their patients heathy should be expanded.

And they could save money by allowing Medicare to negotiate with pharmaceutical makers to lower prices, the way other federal programs and private insurance plans already do.

Denying Medicare to 65- and 66-year-olds might sound good, but it is not real “entitlement reform” and should not be part of a package to avoid the fiscal cliff.