Most American workers must pay into Social Security for at least 10 years to become eligible for Medicare. But government employes who work only one day in January and then retire, having paid only a tiny portion of the Medicare tax, will qualify for the insurance program that takes care of most hospital bills for persons aged 65 and over.

Beginning in January, federal employes, whose jobs are not covered by Social Security, will be required to contribute 1.3 percent of their salary (on amounts up to $35,700) to pay for the Medicare portion of Social Security.

In return, federal service time will be credited toward Medicare eligibility, just as if the employes had worked in Social Security-covered jobs in the private sector paying the full Social Security/Medicare tax for their entire working careers.

When Congress voted to impose the Medicare tax on feds beginning in 1983, it grandfathered in feds who would be retiring shortly after the tax starts up. It said those employes would only have to be on the payroll (and pay the Medicare tax) for a short period of time to qualify for full Medicare benefits at 65.

Congress left it to the Health Care and Financing Administration, an arm of the Department of Health and Human Services, to determine just how long feds would have to work and pay the tax in January to qualify for full Medicare benefits.

HCFA has ruled that federal employes who retire after working only one day in January (and paying the Medicare tax for only one day) will qualify for Medicare.

The prior federal service of those retiring employes will be counted as if they had worked under Social Security jobs in the private sector, and had paid the Medicare tax all that time.

Medicare tax will be an added burden for most government workers, who already contribute 7 percent of their gross annual salary into their retirement fund. But for employes eligible to retire in January, the Medicare tax is a bonanza because they will have to pay only a few dollars to qualify for lifetime hospital insurance protection when they reach age 65.