Those helped would mainly be low-income adults with no children at home, people working jobs that pay little and don't come with health insurance. For uninsured adults below the poverty line, expanded Medicaid is the only way to get coverage under the new law. But middle-class people will be eligible for subsidized private insurance.
Overall, 23 states plus the District of Columbia, are planning to expand their Medicaid programs. About a dozen are undecided.
The nine GOP governors supporting expansion are Jan Brewer in Arizona, Rick Scott in Florida, Terry Branstad in Iowa, Rick Snyder in Michigan, Brian Sandoval in Nevada, Chris Christie in New Jersey, Susana Martinez in New Mexico, Jack Dalrymple in North Dakota and John Kasich in Ohio.
Initially, some observers saw a shift toward pragmatism among Republicans and predicted the governors would get their way. Now experts are not so sure.
Four of the GOP governors have run into real battles. Expansion prospects are flickering in Florida and Michigan. In Ohio, Kasich's legendary deal-making abilities are being tested. In Arizona, Brewer is trying to stare down Republicans in the state House, and the coming week may determine who prevails.
"In the past, that much federal money has brought reluctant parties to the table," said economist Gail Wilensky, a Republican health policy expert who sees flaws in Obama's law but says covering the uninsured is worthwhile. "It is now looking more likely that a number of states will sit out 2014."
Legislators can dig in more easily than governors, adds Alan Weil, executive director of the nonpartisan National Academy for State Health Policy.
"There is a lot of pragmatism involved in the Medicaid decision," Weil explained. "Legislators don't have operational responsibility and tend to adhere more to ideological perspectives."
Arizona's Brewer could be a study in pragmatism.
Once a staunch opponent of "Obamacare," she surprised the political world in January by announcing she would push to expand Medicaid to some 300,000 low-income Arizonans. She called it a fiscally prudent move that would return economic dividends to the state, and stressed that Arizona would back out if Washington reneged on funding.
But Brewer had to battle to get legislation through the Senate, succeeding only with the help of Democrats. The issue could come to a head as early as the coming week in the Arizona House. Brewer seems to have the edge, but her fellow Republicans are unyielding.
"We will continue to fight tooth and nail as far as we can," said Gowan.
In Ohio, Kasich has framed the Medicaid decision as a moral cause, using the language of his Christian beliefs.
The Bible runs his life "not just on Sunday, but just about every day," he said in his annual State of the State address in February.
"I can't look at the disabled, I can't look at the poor, I can't look at the mentally ill, I can't look at the addicted and think we ought to ignore them," he told lawmakers.
But fellow party members don't seem willing to make a leap of faith.
Republicans overwhelmingly control both the Ohio House and Senate. They're leery of expanding government programs and fear being stuck with any long-term costs. The Senate, where Republicans hold 23 of 33 seats, is critical.
The Senate President, Republican Keith Faber, recently told reporters that his members were still divided.
"I have yet to see a proposal that I can tell you there's a majority of my caucus that supports," said Faber.
In Washington, the head of the Catholic Health Association tells the story of a fellow nun who tried to persuade an Ohio GOP legislator to support Kasich's proposal, only to be rebuffed. Sister Carol Keehan, who backs the Medicaid expansion, says the lawmaker told the nun the uninsured could go to community health fairs for basic preventive care.
"He said, 'Sister, they can get their blood pressures taken at the fire station,'" said Keehan, whose organization represents Catholic hospitals. "Would you want your blood pressure taken at the fire station?"