Delivering the party's weekly address, Sen. Thad Cochran of Mississippi said the Affordable Care Act "is not living up to the promises made by its supporters, and it is questionable whether the law will meet its fundamental purpose -- to significantly expand health insurance coverage."
The law was supposed to be fully operational on Jan. 1, he said, but two weeks into the year the administration "continues to struggle to implement the law's burdensome mandates."
Cochran said Republicans in the Senate want to defund or repeal the law.
"If the law can't keep its most basic promise, it should be repealed, and we've introduced legislation to do just that," he said.
"We should go back to the drawing board and draft common sense, bipartisan legislation that will work better for all Americans," he added.
Cochran is serving his sixth term in the Senate. He faces a conservative challenger in the 2014 primary, The Hill reported.