Sen. Mike Enzi, R-Wyo., thinks that if President Obama believes in Obamacare so much, perhaps he should be covered by it.

The three-term senator went on "The Mike Huckabee Show" on Tuesday to promote the amendment sponsored by Sen. David Vitter, R-La., requiring all members of Congress to be covered by the health care law that they passed.

Enzi is a co-sponsor of the amendment.

A version of the amendment had passed as part of the original Affordable Care Act -- inserted into the legislation by Sen. Chuck Grassley, R-Iowa. In August, however, the Office of Personnel Management issued a ruling indicating that members of Congress could still receive government contributions to their health care under the law.

Enzi said that Republicans passed the amendment originally to make sure that members of Congress and their staff didn't get "special treatment.

"We didn't go far enough, because we didn't include the president," Enzi added, indicating that Senate Republicans were working to put Obama and Vice President Joe Biden under Obamacare.

"I can't imagine that the president wouldn't want to be under it — after all, it's named after him," Enzi said.