WASHINGTON — It’s health care brinksmanship, with hundreds of billions of dollars and the well-being of millions of people at stake.

President Barack Obama’s health care law expands Medicaid, the federal-state health program for low-income people, but cost-wary states must decide whether to take the deal.

Turn it down, and governors risk coming off as callous toward their neediest residents. Not to mention the likely second-guessing for walking away from a pot of federal dollars estimated at nearly $1 trillion nationally over a decade.

If the Obama administration were to compromise, say by sweetening the offer to woo a reluctant state, it would face immediate demands from 49 others for similar deals that could run up the tab by tens of billions of dollars.

As state legislatures look ahead to their 2013 sessions, the calculating and the lobbying have already begun.

Conservative opponents of the health care law are leaning on lawmakers to turn down the Medicaid money. Hospitals, doctors’ groups, advocates for the poor, and some business associations are pressing them to accept it.

“Here’s the big thing: The state does not want to expand Medicaid and get stuck with the bill,” said Dr. Bill Hazel, Virginia’s health secretary. “Our legislators do not like to raise taxes to pay for a benefit someone else has promised. The concerns we have ... are around federal solvency and the ability of the federal government to meet its commitment.”

Medicaid covers nearly 60 million low-income and disabled people but differs significantly from state to state. Under the health care law, Medicaid would be expanded on Jan. 1, 2014, to cover people making up to 138 percent of the federal poverty line, or about $15,400 a year for an individual.

About half the 30 million people gaining coverage under the law would do so through Medicaid. Most of the new beneficiaries would be childless adults, but about 2.7 million would be parents with children at home. The federal government would pay the full cost of the first three years of the expansion, gradually phasing down to a 90 percent share.

The Supreme Court said states can turn down the Medicaid expansion. But if a state does so, many of its poorest residents would have no other way to get health insurance. The subsidized private coverage also available under Obama’s law is only for people making more than the poverty level, $11,170 for an individual. For the poor, Medicaid is the only option.

Although the health care law fully funded the Medicaid expansion and Obama has protected the program from cuts, the federal government’s unresolved budget struggles don’t give states much confidence.

Most states, including Republican-led Virginia, are considering their options.

A recent economic analysis by the nonpartisan Kaiser Family Foundation and the Urban Institute found that states will receive more than $9 from Washington for every $1 they spend to expand Medicaid, and a few will actually come out ahead, partly by spending less on charity care. States are commissioning their own studies.

So far, eight states have said they will turn down the expansion, while 13 states plus the District of Columbia have indicated they will accept it. The eight declining are Alabama, Georgia, Louisiana, Maine, Mississippi, Oklahoma, South Carolina, and Texas. Nearly 2.8 million people would remain uninsured in those states, according to Urban Institute estimates, with Texas alone accounting for close to half the total.

Hospitals aren’t taking “no” for an answer in the states that have turned down the expansion. Although South Carolina’s Republican Gov. Nikki Haley has had her say, the Legislature has yet to be heard from, said Thornton Kirby, president of the South Carolina Hospital Association.

Hospitals agreed to Medicare cuts in the health care law, banking on the Medicaid expansion to compensate them.

“We’ve got a significant debate coming in January,” said Kirby. “There are a lot of people tuning in to this issue.”

In Maine, Democrats who gained control of the Legislature in the election are pushing to overcome Republican Gov. Paul LePage’s opposition.

“Obamacare” was once assailed as a job killer by detractors, but on Wednesday in Missouri it was being promoted as the opposite. Missouri’s hospital association in released a study estimating that the economic ripple effects of the Medicaid expansion would actually create 24,000 jobs in the state. The University of Missouri study found that about 160,000 state residents would gain coverage.

“This is not a political issue for us ... this is the real world,” said Joe Pierle, head of the Missouri Primary Care Association, a doctors’ group. “It makes no sense to send our hard-earned federal tax dollars to our neighbors in Illinois.”

By Thursday, Gov. Jay Nixon, D-Mo., had announced his support for the expansion, but he faces a challenge in persuading Republican legislative leaders.

In Florida, where GOP Gov. Rick Scott says he is rethinking his opposition, the state could end up saving money through the Medicaid expansion, said Joan Alker, executive director of the Georgetown University Center for Children and Families, which studied the financing. The reason is that Florida would spend less on a state program for people with catastrophic medical bills.

Back in Washington, Health and Human Services Secretary Kathleen Sebelius says states can take all the time they need to decide. They can even get a free trial, signing up for the first three years of the expansion and dropping out later.

But she hasn’t answered the one question that many states have: Would the Obama administration allow them to expand Medicaid just part way, taking in only people below the poverty line? That means other low-income people currently eligible would be covered entirely on the federal government’s dime, and they would be getting private coverage, which is costlier than Medicaid.

Matt Salo, executive director of the National Association of Medicaid Directors, says he doesn’t think states will get an answer anytime soon.

“This is a game of chicken that we’re seeing,” said Salo. “Are the states bluffing, or are these states really serious? And at what point does the administration rethink things, and decide it’s worth getting half a loaf?”