For now, the federal government pays an average of 57% of the cost of the Medicaid health program for the poor, according to Connolly.
The expansion under Obamacare would make more people eligible but includes 100% federal payment of the additional cost for the first three years, then 95% for the next three years and 90% beginning in 2020, she said.
Opponents such as Jindal contend strapped state governments need to cut back on spending, rather than continuing to fund Medicaid at current levels and eventually picking up a share of the expanded cost.
However, analysts and industry experts say the health care bill's deal is too good for states to resist.
"States will take the federal money, especially in light of longer-term fiscal strains like rising health care and retirement costs," wrote Tracy Gordon, a Brookings Institution economic studies fellow who specializes in state and local public finances, in an online posting Monday.
"Some governors and lawmakers have already said their states will decline to participate in the Medicaid expansion," she wrote. "But eight states have already gotten started on extending eligibility through waivers programs and another three are in the queue. Notwithstanding the highest court in the land, the whole Medicaid package is still an offer states can't refuse."
Connolly noted that health insurance companies and health care providers would push strongly for the Medicaid expansion, which would increase the customer base and reduce the number of uninsured showing up for treatment in emergency rooms.
"I think we need a period to kind of catch our breath and see what kind of conversations take place in the coming months with the governors and the state legislatures and the providers in the states and see what they come up with," she said. "I think that many states will reassess."
Another option is negotiating a fix to the Medicaid provision in light of the Supreme Court ruling. Some Republican governors indicated they would prefer block grants that allow states to decide how to spend their Medicaid dollars.
Obama expressed a willingness to tinker last week in responding to the Supreme Court decision, saying "it's time for us to move forward, to implement and where necessary improve on this law."