The Supreme Court upheld President Barack Obama's health care law on Thursday, but Louisiana Gov. Bobby Jindal, a possible Republican vice presidential contender who has refused to establish a federally mandated health care exchange in his state, said Friday that he will continue to ignore it.

"We're not going to start implementing Obamacare," Jindal said during a conference call with Virginia Gov. Bob McDonnell. "We're committed to working to elect Gov. Romney to repeal Obamacare."

Under the Affordable Care Act, states must set up a health insurance exchange program by Jan. 1, 2014, and will receive grants from the federal government to implement it. Several Republican governors, including both Jindal and McDonnell, have put off setting up the exchanges in the hope that the law would be repealed or struck down by the court. Now that the law has been upheld, Jindal said he won't change course and is looking to presumptive Republican presidential nominee Mitt Romney to lead the repeal effort if he takes office in 2013.

"Here in Louisiana we have not applied for the grants, we have not accepted many of these dollars, we're not implementing the exchanges," Jindal said. "We don't think it makes any sense to implement Obamacare in Louisiana. We're going to do what we can to fight it."

Despite the court ruling, there is still a chance that Republicans in Congress can repeal much of the law next year even if they don't have a filibuster-proof majority in the Senate. Because Chief Justice John Roberts ruled that the mandate to purchase health insurance—one of the key provisions of the law—was a tax, Republicans can use a procedure called "budget reconciliation" to pass a repeal bill that requires only a simple majority to pass. But this scenario relies on the Republicans' ability to win the White House, keep the majority in the House and gain enough seats in the Senate.

On the same conference call on Friday, McDonnell, also considered a contender to become Romney's running mate, said he would "evaluate" his options in Virginia now that the court has upheld the law.

"We don't even know exactly what that federal exchange would look like, so there's still some uncertainty at this point as to what the right course is, and in the next days and weeks we're going to be evaluating the case as well as the options for Virginia," McDonnell said. "I think each state is going to have to weigh that and look at the time frame to determine what to do. But I agree absolutely that the priority right now is to elect a new president and a new Senate so this law can be repealed."

McDonnell, the chairman of the Republican Governors Association, added that he has not yet polled fellow state executives in the GOP about how they plan to proceed after the ruling, but said that most are looking to the election in November for guidance.