House Budget Chairman Tom Price also said after the Court's ruling that he expected Congress to use the process to repeal as much of the ACA as it could. "I would anticipate that we would move in the direction of repealing all of Obamacare that can be repealed through reconciliation," he told reporters.
But if Republicans opt to use reconciliation to go after Obamacare, it means they likely won't be able to use the process to pass something that might actually have a chance of becoming law.
No Republican is likely to vote against repealing the law they hate more than any other, but Rep. Tom Cole, a deputy Republican whip, lamented that the GOP would be forgoing the opportunity to pass something else that would not be dead on arrival when it reaches the White House. "I certainly would favor the repeal of Obamacare, but he's not going to sign that," Cole said. "So to me, it makes more sense to put something that Democrats won't support that he might sign on his desk."
Specifically, Cole named more Medicare means-testing and changes to the way Social Security's benefits are indexed as proposals that Republicans could pursue instead and that Obama might consider approving.
"Both of which would help the country in terms of making it fiscally more secure," said Cole, who made a point to say that the decision largely rests with Senate Republicans. "So why not put something like that, which you might be able to talk the president into, as opposed to something you absolutely won't?"
Others, like Sen. John Thune, have expressed a similar sentiment in the past.
"I'd like to get tax reform done. I think we could do infrastructure in that process. And I think that's something that could actually get enacted.... I mean, we're going to have a lot of Obamacare votes one way or the other," Thune said in January, according to the Associated Press.
The South Dakota Republican did, however, say Thursday after the Court ruling that the Senate "remains committed to repealing this fundamentally broken law and replacing it with patient-centered reforms that work for the American people."
Some members were skeptical that any such compromises could be reached with the White House anyway. "I don't know that he's going to sign anything that we do on reconciliation that would benefit anybody," said Republican Rep Lynn Westmoreland.
And if Republican leadership passed on a reconciliation-to-repeal plan, they'd likely face a revolt from some of the party's most conservative members—a struggle similar to the 2013 fracas in which Sen. Ted Cruz pushed his party to shut down the government unless Democrats agreed to void the law.
Cruz pushed for another repeal effort Thursday. "Absolutely, we should use reconciliation to repeal Obamacare, to place it on President Obama's desk and to force him to veto it," the Texas Republican told reporters. "Because we promised the American people, and it's important that we actually honor the commitments we made to the voters who elected us."