Listen closely and each time a Republican governor decides to expand Medicaid under the Affordable Care Act (ACA), you can hear advocates for President Barack Obama's health reform law and the low-income insurance program softly whisper: We told you so.

In the wake of the U.S. Supreme Court’s decision last June to give states the option of expanding Medicaid, most GOP governors and legislators rejected the idea, which would increase eligibility to 133 percent of the federal poverty level and add up to 17 million to state Medicaid rolls. But lobbying from key stakeholders (hospitals and doctors chief among them) and the possibility of missing out on hundreds of millions of federal dollars has softened that opposition.

Arizona’s Jan Brewer, Nevada’s Brian Sandoval and New Mexico’s Susana Martinez were the first Republican governors to break from the national party and embrace the expansion -- and they probably won’t be the last. Their stated reasons for their change of heart echo what policy analysts and advocates told Governing they would be long before the governors made up their minds.

It all comes down to dollar signs. If states choose to expand Medicaid, the federal government will cover 100 percent of the costs from 2014 to 2016. The feds' contribution will begin to decrease in 2017, but will never be less than 90 percent, under the ACA.

“For many states, it's going to be very difficult for them to leave that money on the table,” Linda Blumberg, a health economist and senior fellow at the Urban Institute, told Governing on June 28, the day of the Supreme Court ruling. “I think there is going to be considerable financial pressure -- both from providers and the reality of state budgets -- to go with this.”

A few months later, Len Nichols, director of the Center for Health Policy Research and Ethics at George Mason University, said the same thing. He pointed to a past example: the creation of Medicaid back in 1965. In the program's first year, only about half of the states signed on. But within a few years, 49 had come onboard (Arizona was the last to join in 1982). Political will gave way to fiscal realities.

“They all did the math and had to ask, ‘Why am I leaving all this money on the table?’” Nichols told Governing. “It’s a deal that most states will not be able to refuse in the long run. That’s why the administration is acting confident that all states will come in.”

Now those premonitions are turning out to be true.

Sandoval (a 2012 Governing Public Official of the Year) was the first Republican governor to officially embrace the Medicaid expansion, back in mid-December. It wasn’t exactly an enthusiastic endorsement -- Nevada officials warned that it could place a burden on the state budget when the 100 percent federal match starts to phase down to 90 percent by 2017 -- but there was also recognition that it would be unwise to forego an infusion of federal dollars into the state economy. Sandoval’s office estimates that the expansion will enroll 78,000 people and bring more than $700 million federal dollars into the state over the first three years.

“That's a massive leverage of federal dollars," said Jeff Mohlenkamp, Sandoval’s budget director. “Considering how many federal dollars we are leveraging, the cost (of expansion) is fairly small.”

This week, Brewer made headlines nationwide when she sanctioned the Medicaid expansion in her State of the State address. Her reasoning followed another familiar line from those who were confident that most states would expand: It will be good for hospitals and other health-care providers. Governing reported in the days after the Supreme Court decision that hospitals, traditionally one of the strongest lobbying groups in statehouses, would be pushing hard for expansion. One of their favorite talking points is uncompensated care. If more people are covered by Medicaid, hospitals will perform fewer unpaid services that usually get passed onto insurance premiums and taxpayers to fund.

Brewer cited all of the above in her reasons for backing the expansion.

“We will protect rural and safety-net hospitals from being pushed to the brink by growing their cost in caring for the uninsured,’’ she said. “Health-care premiums are raised year after year to account for expenses incurred by our hospitals.”

Likewise, Martinez's announcement underscored both motivations, according to the Albuquerque Journal. Expanding Medicaid will be budget-neutral, the governor said, and her decision was praised by New Mexico's health-care providers.

“It does appear to be clear that expanding Medicaid would not jeopardize the state’s long-term budget outlook,” Martinez said. “We will not only save money each year, but can expect revenue increases, and that will offset the cost of providing these services in the future.”

More movement on the Medicaid expansion is likely in the coming weeks, as governors deliver their proposed budgets and state legislative sessions get underway. Democratic-controlled states are expected to sign off on the expansion with relative ease, and there's reason to think that more GOP governors will follow in the path of Brewer, Sandoval and Martinez.

Texas Gov. Rick Perry has become the national figure for opposing all implementation of the ACA, especially the Medicaid expansion. But at a National Conference of State Legislatures forum in November, a Texas legislator said that Perry’s staff was quietly meeting with lawmakers to at least explore the possibility of expanding. Wisconsin Gov. Scott Walker, another outspoken opponent of the law, declined to outright denounce the expansion in his State of the State address (which is becoming a popular forum for governors to make their announcement). And in Ohio, where Gov. John Kasich has also stopped short of saying his state won’t expand, a nonpartisan study estimates that the state could actually reap $1.4 billion in saved spending and new tax revenue under the expansion, according to the Associated Press.

With those kinds of numbers at stake, it’s easy to understand why the Republican tune on the Medicaid expansion is changing. As George Mason’s Nichols told Governing last year: “Usually, in the history of the world, math trumps ideology.”