Leading Republican senators on Wednesday introduced a bill to repeal one of Obamacare’s most unpopular provisions – the individual mandate that requires most Americans to obtain health insurance or pay a penalty.

Senator Orrin Hatch, chairman of the Senate Finance Committee, and Senator Lamar Alexander, who heads the Senate Health, Education, Labor and Pensions Committee, announced the three-paragraph bill titled, the American Liberty Restoration Act, with backing from 20 other Republican co-sponsors.

It was the first time that legislation to eliminate the mandate, a linchpin of President Barack Obama’s Affordable Care Act, has been introduced by a Senate majority party.

The mandate survived a 2012 U.S. Supreme Court challenge seeking to overturn it on constitutional grounds. It has now become part of a new Republican effort to chip away at the legislative underpinnings of the law known as Obamacare.

Aides said the bill should eventually come to a vote. But it was unclear whether the measure would overcome potential blocking tactics by Democrats.

The White House had no immediate comment. But Obama, who vowed in Tuesday’s State of the Union address to oppose efforts to roll back his policies, would be expected to veto the measure. “The individual mandate is a line I can’t cross,” the president said at a news conference in November.

Analysts, insurers and healthcare reform advocates have long described the individual mandate as a vital lever for encouraging young healthy consumers to sign up for health coverage under Obamacare. Its loss, they say, could unsettle insurance markets and cause coverage costs to rise sharply.

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Jeffrey R. Ungvary President