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After nearly three years of legal and political threats that keptPresident Obama’s health care law in a constant state of uncertainty, his re-election on Tuesday all but guarantees that the historic legislation will survive.

Now comes another big hurdle: making it work.

The election came just 10 days before a critical deadline for states in carrying out the law, and many that were waiting for the outcome must now hustle to comply. Such efforts will coincide with epic negotiations between Mr. Obama and Congress over federal spending and taxes, where the administration will inevitably face pressure to scale back some of the costliest provisions of the law.

Mr. Obama faces crucial choices about strategy that could determine the success of the health care overhaul: Will the administration, for example, try to address the concerns of insurers, employers and some consumer groups who worry that the law’s requirements could increase premiums? Or will it insist on the stringent standards favored by liberal policy advocates inside and outside the government?

But for now — with Democrats retaining control of the Senate and Mitt Romney’s vow to “repeal and replace” the law no longer a threat — supporters are exulting.

“For our district and for our country, the debate on Obamacare is over,” declared Bill Foster, a Democrat elected Tuesday to the House from a suburban Chicago district.

Many supporters feel one of Mr. Obama’s most important tasks will be to step up efforts to promote and explain the law to a public that remains sharply divided and confused about it. In exit polls on Tuesday, nearly half of voters said the law should be either partly or fully repealed.

“There is still a tremendous amount of disinformation out there,” said Jeff Goldsmith, a health industry analyst based in Virginia. “If you actually are going to implement this law, people need to know what’s in it — not just the puppies-and-ice-cream parts, but ‘Here are the broader social changes intended and how they can help you.’ ”

Already, advocacy groups eager for the law to succeed have shifted into a higher gear. One such group, Families USA, held a conference call on Thursday with about 300 advocates around the country to strategize about next steps, said Ronald F. Pollack, the group’s executive director. Enroll America, a sister organization, will hold focus groups next week in Ohio, Pennsylvania and Texas to collect ideas for a public education campaign.

Much depends on the states as they decide in the coming weeks and months whether to build online marketplaces known as insurance exchanges, where individuals and small businesses can shop for health plans, and whether to expand their Medicaid programs to reach many more low-income people.

The clock is ticking on the exchange question in particular: states have until next Friday to decide whether they will build their own exchange or let the federal government run one for them. Some states have asked the administration for more time.

So far, only about 15 states and the District of Columbia have created the framework for exchanges through legislation or executive orders; three others have committed to running exchanges in partnership with the federal government. A number of Republican governors, including those in Arizona, Idaho, New Jersey, Virginia and Tennessee, had said they would decide after the election, giving themselves only a 10-day window before the deadline.

“I would expect that starting today there are a significant number of fascinating conversations going on behind closed doors in state capitols all over America,” said John McDonough, a professor of public health at Harvard who helped draft the law.

With deficit-reduction talks beginning in Washington next week, some observers believe that the law’s most expensive provisions — like federal subsidies to help families with incomes up to 400 percent of the poverty level pay their insurance premiums — could be scaled back in the name of deficit reduction.

“We know folks on the Hill are talking about this already,” said David Smith, an analyst at Leavitt Partners, a consulting firm that advises states on the law. “There are a lot of competing factors, but they have to find the savings and we believe health care will be one of the places where they will go.”