Despite President Obama's victory, Republican governors say they're not caving in on carrying out the Affordable Care Act - or as they've derisively dubbed it, "Obamacare."

Several governors have announced that they would not set up state health care exchanges from which residents can select a health care plan, a requirement of the signature piece of legislation from Obama's first term, even though Obama's re-election made the Affordable Care Act the law of the land and any refusal to set up the exchanges is largely symbolic.

On Thursday, Secretary of Health Human Services Kathleen Sibelius extended the deadline to decide whether they will set up these exchanges from Nov. 16 to Dec. 14.

This week several governors announced they're opting out.

On Thursday, South Carolina governor and rising Republican star Nikki Haley sent a letter to Sebelius on Thursday saying that South Carolina "should not and will not set up a state-based health care exchange."

Several other Republican governors, including Louisiana Gov. Bobby Jindal, a GOP leader who is frequently cited as a potential candidate in 2016, and Alabama Gov. Robert Bentley announced that their states would also not set up an exchange.

"I am not going to set up a state-based exchange that will create a tax burden of up to $50 million on the people of Alabama," Bentley said Tuesday.

Other states where the governors have made similar declarations include Kansas and Alaska. In Missouri, the Democratic governor announced on Thursday that the state would not set up an exchange either, but that announcement resulted from a ballot measure that forbade the governor from moving forward with an exchange without the approval of the state's legislature, and Republicans control Missouri's state legislature.

Wisconsin Gov. Scott Walker has said that he will make his announcement on Friday.

So what do these refusals mean for the future of the health care law? Not much, it seems, as the health insurance exchanges will be set up in these states anyway.

Under the law, if a state falls behind or opts not to set up the exchange, the federal government, specifically the Department of Health and Human Services, steps in and sets up the exchange. That would not likely be well-received by Republican governors either, but the law forces each state's executive to make a decision one way or the other.

"If the state decides not to establish an exchange, then the federal government establishes the exchange for them. So it's kind of a pick-your-poison scenario, if you will," said Renee M. Landers, a professor of law at Suffolk University Law School in Boston.

The potential for state executives to opt out of this portion of the law had been anticipated for some time. Almost immediately after the Supreme Court announced its ruling on the Affordable Care Act last June, several governors, including Jindal and Walker, said they would wait until after the election to take any sort of action on the law.

ABC News' Sarah Parnass and Shushannah Walshe contributed to this report.