WASHINGTON — The long slog has turned into a sprint. President Barack Obama’s health care law survived the Supreme Court and the election; now the uninsured can sign up for coverage in about 11 months.

Even the government’s top-ranking Republican, House Speaker John Boehner of Ohio, said Thursday that “Obamacare is the law of the land.” But not all hurdles have been cleared.

Republican governors who opposed the law have to decide whether it’s better for their states to now help carry it out. The administration could stumble carrying out the complex legislation, or get tripped up if budget talks with Congress lead to scaling back the plan.

“We are out of the political gamesmanship and into the reality,” said Sandy Praeger, Kansas’ Republican insurance commissioner. Next week, states have to say if they’re committed to building the framework for delivering health insurance to millions.

“We are still going to be struggling through the politics, and there are important policy hurdles and logistical challenges,” said Andrew Hyman of the nonpartisan Robert Wood Johnson Foundation, helping states carry out the law. “But we are on a very positive trajectory.”

Instead of being dismantled by a Republican president and Congress, Obama’s law is now on track to take its place alongside Medicare and Medicaid. The action starts right away.

A week from Friday, states must notify Washington if they’ll be setting up new health insurance markets, called exchanges, in which millions of households and small businesses will shop for private coverage. The Health and Human Services Department will run the exchanges in states that aren’t ready or willing.

Open enrollment for exchange plans is scheduled to start Oct. 1, 2013, and coverage will be effective Jan. 1, 2014.

In all, more than 30 million uninsured people are expected to gain coverage under the law. About half will get private insurance through the exchanges, with most receiving government help to pay premiums.

The rest, mainly low-income adults without children at home, will be covered through an expansion of Medicaid. While the federal government will pay virtually all the additional Medicaid costs, the Supreme Court gave states the leeway to opt out of the expansion. That adds to the uncertainty over how the law will be carried out.

A steadying force within the administration is likely to be HHS Secretary Kathleen Sebelius. The former Kansas governor has said she wants to stay until the law is fully enacted.

Governors will be the main counterparts to Sebelius, and Republicans are leading more than half the states.

Some, like Rick Perry of Texas and Rick Scott of Florida, have drawn a line against helping carry out Obama’s law. In other states, voters have endorsed a hard stance. Missouri voters passed a ballot measure Tuesday that would prohibit establishment of a health insurance exchange unless the Legislature approves. State-level challenges to the federal law will continue to percolate.

Other GOP governors have been on the fence, awaiting the outcome of the election. All eyes will be on pragmatists like Chris Christie of New Jersey and Bob McDonnell of Virginia, whose states have done considerable planning to set up exchanges.

“Republican governors are at the center of the health care universe right now,” said Michael Ramlet, health policy director at the American Action Forum, a conservative think tank. “They do not have a uniform position.”

Virginia’s McDonnell, in a rebuff to the administration, said in an interview published Thursday his state would not set up its own exchange, defaulting to a federally run one. McDonnell left open the possibility Virginia might later change course.

Some governors whose states aren’t ready to run exchanges are considering the administration’s fallback offer to run the new markets through a partnership.

“The real question for Republican governors is: ‘Are you going to let the feds come into your state?”’ Ramlet said. “The question for the Obama administration is whether they are going to have more flexibility.”

Major regulations are due shortly covering such issues as exchange operations, benefits and protections for people with pre-existing health problems. That could signal the administration’s willingness to compromise.

A check by The Associated Press found 17 states and the District of Columbia on track to setting up their own exchanges, while 10 have decided not to do so. The federal government could end up running the show in half or more of the states.

The states on track include California, Colorado, Connecticut, Hawaii, Kentucky, Maryland, Massachusetts, Minnesota, Mississippi, Nevada, New York, Oregon, Rhode Island, Utah, Vermont, Washington, and West Virginia.

Not setting up exchanges are Alaska, Florida, Louisiana, Maine, New Hampshire, South Carolina, South Dakota, Texas, Virginia, and Wisconsin. Missouri and others are likely to join the list.

A recent AP poll found that 63 percent of Americans want states to run the exchanges, with 32 percent favoring federal control.

GOP governors are also seeking flexibility on expanding Medicaid. They are pressing Sebelius on whether the administration will approve partial, less costly expansions, more attractive to cash-pressed states.

As far as Medicaid, 11 states and the District of Columbia have indicated they will expand their programs, while six have said they will not. That leaves more than 30 undecided.

The states definitely expanding Medicaid include California, Connecticut, Delaware, Hawaii, Illinois, Maryland, Massachusetts, Minnesota, New York, Vermont, and Washington. Those declining include Florida, Georgia, Louisiana, Mississippi, South Carolina, and Texas.

On Capitol Hill, Republicans say if a budget deal is going to include tax increases, it must also come with cuts to the health care law, or money-saving delays in its implementation.

While major changes can’t be ruled out, they don’t seem very likely to former Senate Majority Leader Tom Daschle, D-S.D., who is close to the administration.

“I think Democrats are increasingly emboldened about the health care act,” Daschle said. “The president won re-election partly by defending it. There is a new dynamic around the health care effort.”

Republican attempts to amend the law will continue, he said, but outright repeal is no longer a possibility.

Speaker Boehner seemed to second that in an interview with ABC News. Asked if he will make another attempt to fully repeal Obama’s law, he responded, “Well, I think the election changes that.”

But he added that parts of the health care law are very expensive and difficult to carry out and “everything has to be on the table” in budget negotiations. Later, spokesman Kevin Smith said that Boehner is “still committed to full repeal.”