A federal appeals court ruled Tuesday that seniors who receive Social Security cannot reject their legal right to Medicare benefits, in a rare case of Americans suing to get out of a government entitlement.

Former House Majority Leader Dick Armey is among the five senior citizens who sued to stop their automatic eligibility for Medicare. But the appeals court ruled in a split decision that the law gives them no way to opt out of their eligibility if they want to keep their Social Security benefits.

Armey, a Texas Republican, and his co-plaintiffs say their private insurers limit their coverage because they are eligible for Medicare, but they would prefer the coverage from their private insurers.

"We understand plaintiffs' frustration with their insurance situation and appreciate their desire for better private insurance coverage," Judge Brett Kavanaugh wrote in a majority opinion joined by Douglas Ginsburg, both Republican appointees. But they agreed with the Obama administration that the law says those over age 65 who enroll in Social Security are automatically entitled to Medicare Part A, which covers services including hospital, nursing home care, hospice and home health care.

The case is being funded by a group called The Fund For Personal Liberty, which says its purpose is to take on burdensome government regulations. Attorney Kent Brown, who argued the case for the plaintiffs, say they want to keep their Social Security because they believe they earned it, but none of them want Medicare Part A.