In the span of a month, some of Obamacare's most ardent opponents have come to embrace one of the law's most crucial programs: The Medicaid expansion.

With seven Republican governors now signed up, most recently Florida's Rick Scott on Wednesday, Republican-led states now account for nearly one-third of those expected to take the federal government's money to expand Medicaid up to 133 percent of the federal poverty line.

These same governors have, however, also eschewed another big Obamacare component: The exchanges. The three most recent Medicaid expansion converts—Florida's Rick Scott, Michigan's Rick Snyder and Ohio's John Kasich—have all rejected the idea of setting up the marketplace, leaving it to the feds to do the work, instead (Michigan is splitting the difference and will run its market in partnership with the feds).

Why embrace one part of the health care law -- a single-payer system that will stretch President Obama's law to cover millions more Americans -- while ditching the other more market-oriented aspect? It likely has to do with the big consequences for a governor who chooses not to expand Medicaid—versus the tiny reward with setting up a very complex insurance marketplace.

There's not a lot riding on governors' decision to build a health insurance exchange. The marketplaces certainly are important to the Affordable Care Act: They're the online portals where millions of Americans will ultimately purchase health insurance, the key vehicle for delivering the health law's insurance expansion.

Building a health exchange is a huge undertaking. Between connecting disparate government computer systems and creating a seamless shopping experience, industry analysts say that this process should take two or three years.

If governors cram it into 10 months, and the final product comes out subpar, they would likely take the blame.  But if a governor doesn't go through with building one, the federal government swoops in. It has promised that every state will have an insurance exchange by Oct. 1, the date that the new markets will open for enrollment.

The federal government may pull the exchanges off without a hitch—or, as with many new programs, the marketplaces could launch with glitches. Either way, the federal government is now at the helm, and it's the one responsible for whatever failures or successes the exchange experiences. This could explain why even some Democratic governors (Jay Nixon in Missouri and Steve Bullock in Montana) have agreed to let the feds run the show.

That's the story with the exchanges: There's little political upside to building one, but lots of potential fallout. On the Medicaid expansion, the calculus is completely different. The federal government cannot provide a back-up Medicaid expansion—and governors are deciding whether to extend health insurance to hundreds of thousands of their residents.

The Urban Institute ran the numbers and found that, if all states participate in the Medicaid expansion, it would bring $952 billion in new federal dollars to state Medicaid programs and cover 21.3 million people. For the first three years, the federal government will also cover all costs for those newly-eligible enrollees. That's way more than it usually pays for Medicaid: The federal government typically foots somewhere between 50 and 70 percent of a state's Medicaid bills, depending on poverty levels.

For states, the implications of this could be huge: Nearly $1 trillion in new federal funding would cover many of the medical bills that, right now, go unpaid. They're usually picked up by hospitals or local governments, which run indigent care programs.

Or, as Scott put it in a press conference last night, "While the federal government is committed to paying 100 percent of the costs, I cannot deny Floridians who need access to health care."

If Scott did not opt-into the new program, he foresaw himself having to explain to Floridians why their federal tax dollars would fund a Medicaid expansion in other states, but not the one where they lived.

"Our options are either having Floridians pay to fund this program in other states while denying health care to our citizens, or using federal funding to help some of the poorest in the state," Scott said.

Scott sided with the latter option, even when declining to build a health insurance exchange. He has no back-up option, a lot of downside to sending federal tax dollars elsewhere—and a lot of upside in bringing billions in Medicaid funding into his state.

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