Republicans are scrambling to forge a health-care compromise after their effort to undo the Affordable Care Act, also known as Obamacare, fell apart in the Senate last week. One particularly thorny issue is the plight of people in the lower middle class who have benefited from an expansion of Medicaid under the Affordable Care Act, but who might go without that coverage under past versions of the GOP bill.

The issue, which has made several moderate senators reluctant to support the legislation, is not an easy one to solve. Some Republicans have reportedly talked about spending more money to help this group pay for private insurance — as much as $200 billion, Bloomberg reported.

Yet a new analysis published Monday warns that amount will not be nearly enough.

The report, from the nonpartisan Urban Institute, estimates that $200 billion would cover additional benefits for this group for only a couple of years. After that, they would have to choose between buying costly private insurance with hefty deductibles or going without coverage. Republicans might have trouble coming up with more money to extend those benefits.

“The funds that they’re talking about — $200 billion — is not going to get you much more than two years," said economist Linda Blumberg, one of the authors of the report. "It could get you less than that."

The group in question are those who became eligible for Medicaid, the federal insurance program that covers many poor households, pregnant women and elderly residents of nursing homes, as a result of the Affordable Care Act. A larger group of people — a group that is poor or nearly poor but would not have qualified for Medicaid previously — were able to join the program.

The Supreme Court gave states authority to choose whether to expand Medicaid under the Affordable Care Act for their residents, and while policymakers in politically liberal or moderate states were more likely to take advantage of the more generous program, many of the states that did are represented by Republicans in the Senate. The GOP bill to undo the Affordable Care Act would also undo the expansion of benefits to this group of about 13 million people, which is cause for concern for some Republican senators.

To get around the issue, GOP policymakers have discussed helping those who could lose coverage through Medicaid buy private insurance instead. The proposal would dedicate federal funds to help people in this group pay their premiums and out-of-pocket costs, according to Bloomberg. Republicans are calling it a “wraparound,” combining federal benefits with private insurance to make it more affordable.

The Urban Institute predicts that doing so would cost $76 billion in the first year alone, and potentially over $100 billion, depending on what extent states try to take advantage of the additional funds. Coming up with that much money could be a challenge for Republicans.

Borrowing the money is probably not an option. Because of the Senate's rules, the health-care bill could be subject to a filibuster if it would increase borrowing over the long term, and Republicans want to prevent Democrats from using that tactic.

The most recent version of the GOP bill was estimated to save the federal government about $420 billion over 10 years by reducing federal spending on health benefits, according to the nonpartisan Congressional Budget Office. Republicans could restore some of that money in the form of additional benefits for those at risk of losing Medicaid coverage.

Alternatively, GOP lawmakers could reallocate other spending in that version of the bill. For instance, the bill would set aside a fund that states might be able to use in a variety of ways to help treat sick residents.

States could dedicate some of that money to paying for these benefits — although doing so would leave less available for protecting insurers from risk through federal reinsurance, resulting in stiffer premiums across the individual market. That, in turn, would drive up spending again, because under the GOP plan, the federal government will continue paying for a portion of individual consumers' premiums to help them buy private insurance.

Another option would be to maintain some of the Affordable Care Act taxes that they proposed repealing in that version of the bill, which amount to $484 billion over a decade. Keeping the taxes in force would generate more money, but Republicans would risk the charge that they are not truly delivering on their promise to undo the Affordable Care Act. They could alienate lobbyists for insurance companies and the medical industry, which are paying the bulk of those taxes.

Maybe Republicans will come up with some clever solution to the problem, although they do not have much time. They have not yet settled on a new proposal, although voting is scheduled for Tuesday in the Senate.

“We’re guessing as to what this proposal would look like, because there's nothing written down on paper that’s public,” Blumberg said.