The House is set to vote Tuesday on a bill to repeal Obamacare, one of the top priorities of the more conservative members of the Republican-controlled Congress, the influential conservative group Heritage Action for America said Monday. But the vote -- the 56th the House is holding on repealing the Affordable Care Act -- is doomed by the GOP not having enough votes to counter a presidential veto threatened by President Barack Obama. 

The bill, H.R. 596, is sponsored by U.S. Rep. Bradley Byrne, R-Ala., who said in a statement last week that it was a “great accomplishment” for his bill to be considered by House leadership. Byrne is just in his first full term.

“I am very pleased the House will vote [Tuesday] on a bill to repeal Obamacare, and I am especially pleased it is my legislation,” he said. “In addition to repealing the law which is making life harder for so many Americans, the bill instructs the relevant committees in the House to come forward with an alternative, patient-centered solution to help fix our health care system.”

H.R. 596 isn't a major threat to dismantle Obamacare. The legislation is a way for establishment Republicans to appease more conservative members by letting them vote on the bill.  “We’re just getting it out of the way," a GOP aide told the Washington Examiner about H.R. 596.

The repeal of Obamacare in general is uncertain because Republicans are split over whether to fully repeal Obamacare or amend it, and they don't have a veto-proof majority; this is the 56th time that the House is voting to repeal the health care law, according to the Atlantic. Tea party groups will be angered by the establishment if Obamacare isn’t gutted. On the other hand, establishment Republicans may face heat from millions of constituents who benefit from the health care law, Politico noted.

Meanwhile, the U.S. Supreme Court is scheduled next month to hear arguments on a key provision of Obamacare. The court will weigh in on whether tax credit subsidies for health insurance should be given to everyone under the law or only those who obtain insurance through state exchanges, according to SCOTUSblog. The GOP is still considering its strategy for how to proceed if the court rules the subsidies shouldn’t be given to citizens in states that didn’t set up their own exchanges, Politico reported.

“We want to be responsible about repairing any damage that Obamacare does,” U.S. Sen. Lamar Alexander, R-Tenn, who is involved in weekly GOP talks on strategy, told Politico. “If it creates a shock to the system by causing 5 million Americans suddenly to put their insurance and their subsidies at risk, then we need to think if there’s anything we need to do. Maybe there’s not.”