Republicans are picking through the ruins of their Obamacare repeal plans following Thursday's Supreme Court ruling upholding the law.

They're left with few viable options for getting rid of the health care reforms, and probably none unless they win the White House in 2016 and retain control of Congress.

GOP leaders quickly asserted that they will continue fighting for repeal despite the Court upholding federal subsidies in states that did not create their own health insurance exchanges.

"One thing that today's ruling does confirm is that we must repeal and replace this fundamentally flawed law," said House Majority Leader Kevin McCarthy, R-Calif. "The House will continue to work toward a patient-centered solution and to help those who have felt the hardships this law has caused."

But Republicans can't do much, even though they control the House and Senate, because President Obama would veto any measure undoing his signature legislation.

"We've got more work to do," Obama acknowledged after the ruling was announced. "But what we're not going to do is unravel what has now been woven into the fabric of America."

Democrats in Congress put it more bluntly to the GOP. "I think they should get real and forget about Obamacare," Senate Minority Leader Harry Reid, D-Nev., said.

But Republicans plan to trudge on in their years-long battle to topple the law. GOP members have most recently plotted a path to repeal that would use a parliamentary tactic in the budget process known as reconciliation, which would allow the Senate to vote down the law with just 51 votes, rather than the typical 60.

While such a move would send repeal legislation to the president's desk, there are not enough Republicans in Congress to override a veto, so it would never become law.

"Absent a cooperative president," Senate Finance Committee Chairman Orrin Hatch, R-Utah, acknowledged, "the negative consequences of Obamacare will continue."

Republicans insisted Thursday that even though it faces a certain veto, legislation to repeal the law through reconciliation remains a top possibility and could still happen this year.

"That's being worked out," a top GOP Senate aide told the Washington Examiner. "No specifics yet."

House Republicans say they will continue with another lawsuit against the law. The suit challenges the Obama administration's use of "risk corridor" funding to pay insurance companies billions of dollars to keep their rates low.

"They are paying insurers out of an account that's never been appropriated," House Speaker John Boehner, R-Ohio, said Thursday. "They've taken money from elsewhere in the law to do this. I think it violates the Constitution. It certainly violates Congress's prerogative to appropriate funds."

Republicans are also working on a second path to repeal, one that would undermine the law bit by bit.

The House has passed dozens of measures over the past few years that would undo sections of the law and now that the Senate is controlled by Republicans, some have a real chance of making it to Obama's desk. Atop the list is a bill to repeal the law's medical device tax.

The House voted earlier this month to end the 2.3 percent tax on medical devices, which critics say increases consumer costs and discourages innovation in the field. It was implemented in January 2013 as part of Obamacare and is supposed to raise $20 billion by the end of the decade, all of it meant to help pay for the healthcare law.

The Senate has introduced a companion measure and will take it up this year, a Senate GOP leadership aide said. Enough Democrats back its repeal that Congress could override a presidential veto, but there could be a dispute over how to pay for it.

This week, the House voted 244-154 to repeal Obamacare's Independent Payment Advisory Board, which was created to help achieve savings in Medicare but is feared by opponents to be a tool for rationing medical care. The board has no members yet and is not active. Only 11 Democrats voted for the bill, which now heads to the Senate where it it could be filibustered by Democrats in that chamber.

With no repeal in sight, Republicans now get more time to work on a unified plan to replace the law. Several proposals have been introduced, but none have been debated in either chamber.

The Republican Study Committee, a group of about 70 conservative members, released an Obamacare replacement plan earlier this month. Rep. Tom Price also recently introduced a healthcare reform plan.

"Our focus is going to shift to broader replacement policy," said Brendan Buck, spokesman for the Ways and Means Committee.

But while Republicans have long promised to vote on replacing the Affordable Care Act, they've yet failed to rally around one plan.

Republicans in the House and Senate huddled last week to devise a back up plan for people who use health care subsidies, in the event the Supreme Court ruled them to be illegal.

Such a ruling would have thrown the future of the health care law in serious doubt. Republicans claim they were ready to act with a unified proposal to help those who depend on its subsidies, but they didn't reveal it.

"Now it's not necessary," Boehner said.