Updated

Several Republican governors, in what could be their last symbolic stand against ObamaCare, announced Friday that they will not set up a state-based marketplace for selling health insurance.

A total of 20 states have now decided not to implement their own exchanges -- which could also mean increased costs for the federal government.

The governors of Wisconsin and Ohio joined Texas Gov. Rick Perry and others in confirming that they will not establish so-called "health insurance exchanges," which are set to launch in January 2014. Under the federal health care overhaul, these exchanges will act as virtual markets where people and small businesses can shop for private coverage in a regulated environment. Many will also be eligible for government subsidies.

The governors' move does not stop those exchanges from being implemented. Rather, it kicks the project back to the federal government to run with regard to those states. While a number of states, largely those run by Democrats, will establish their own exchanges, Republicans who declined argued that it wasn't worth the cost and resources to set up a marketplace that would be under the thumb of the federal government anyway.

"As long as the federal government has the ability to force unknown mandates and costs upon our citizens, while retaining the sole power in approving what an exchange looks like, the notion of a state exchange is merely an illusion," Perry wrote in a letter to Health and Human Services Secretary Kathleen Sebelius. "It would not be fiscally responsible to put hard-working Texans on the financial hook for an unknown amount of money to operate a system under rules that have not even been written."

Wisconsin Gov. Scott Walker said the same, writing in a letter to Sebelius Friday that "no matter which option is chosen, Wisconsin taxpayers will not have meaningful control over the health care policies and services sold to Wisconsin residents." With that in mind, he wrote, the state has decided not to build its own system. Ohio Gov. John Kasich echoed that point of view.

Republican governors have been largely opposed to the health care law anyway. But for months, they were effectively waiting to see if the Supreme Court would overturn it or whether Obama would lose re-election and potentially leave an opening to repeal it. Neither of those things happened.

Walker was among those who stopped implementation last year on the hopes the law would be overturned either by the U.S. Supreme Court or Republicans following the November election.

Thursday evening, the Obama administration responded to a request for more time from Republican governors on the exchange question by granting states a month's extension, until Dec. 14.

A few states have signaled they want to partner with the federal government, as opposed to running it themselves or handing the reins to Washington. Those states would handle consumer issues and oversight of health plans in the exchanges, while the feds do the heavy lifting by enrolling individuals for coverage and determining who's eligible for government assistance. Among these states are Arkansas and North Carolina.

The number of partnership states could grow significantly, since the Obama administration has given states until next February to decide on that option.

Obama's election victory virtually guaranteed the survival of his health care law, which is eventually expected to provide coverage to more than 30 million people through the exchanges and expanded Medicaid programs. It was the final hurdle, after the Supreme Court upheld a legal challenge from 26 states. In the aftermath of the election, some Republican state leaders say it's time to accept the law.

"I don't like it; I would not vote for it; I think it needs to be repealed. But it is the law," said Mississippi Insurance Commissioner Mike Chaney, after announcing that his state wants to set up its own exchange. "If you default to the federal government, you forever give the keys to the state's health insurance market to the federal government."

Traditionally, states have regulated the private health insurance market.

But other Republican-led states say they don't have enough information to make a decision at this point and are clamoring for the Obama administration to release major regulations that have been bottled up for months.

"States are struggling with many unanswered questions and are not able to make comprehensive far-reaching decisions prudently," Govs. Bob McDonnell of Virginia and Bobby Jindal of Louisiana wrote Obama earlier this week. They asked for a meeting with the president, as well as a postponement of the original Nov. 16 deadline.

Some of their main concerns are hidden costs of operating the exchanges and the sheer bureaucratic complexity of the new system. The Obama administration has steadfastly maintained it will not postpone the Jan. 1, 2014, launch date for the law's coverage expansion. Open enrollment for exchange plans will begin even sooner, Oct. 1, 2013.

The Associated Press contributed to this report.