Poor adults in red states that expanded Medicaid under Obamacare were twice as likely to say the law had helped them than harmed them, according to a study released Wednesday that underscores the challenge before Republicans who want to revamp the program as part of their repeal-and-replace strategy.

Researchers looked at four states — Arkansas, Kentucky, Louisiana and Texas — that voted for President Trump by wide margins, though only the first three accepted an influx of federal funds to expand Medicaid, the government insurance program for the poor, under his predecessor.

“Overall, twice as many respondents in the three expansion states reported being helped by the law than hurt by it, whereas in Texas more respondents thought the law had hurt them than thought it had helped them,” researchers Benjamin D. Sommers and Arnold M. Epstein said in The New England Journal of Medicine.

Republicans say Obamacare’s web-based insurance exchanges are collapsing under the weight of soaring premiums and dwindling plans choice, so it’s important to repeal the law “root and branch,” and replace it with market-oriented reforms.

Yet a key sticking point is what to do about the 31 states that expanded Medicaid under the law, including 13 that Mr. Trump won in November.

Under Obamacare states could expand Medicaid to those making up to 138 percent of the federal poverty level. The federal government picked up the full cost of expansion in 2014-16, though its share will slide to 90 percent by 2020 and beyond.

Ohio Gov. John Kasich, a Republican, has urged Congress to let states like his retain the expansion and federal funding, saying it’s reduced the number of uninsured and pricey ER visits. He said federal lawmakers seeking changes should roll back the expansion instead of repealing it.

Indeed, with roughly 12 million covered since expansion, it will be difficult for Capitol Hill Republicans to turn back completely.

“I think that this is one of the most difficult issues that they’re going to have to tackle. Obviously, I think governor[s of] each [state] have a vested interest based on the decision they made with respect to Medicaid expansion,” said Lanhee J. Chen, a fellow at Stanford University’s Hoover Institute who advised 2012 GOP nominee Mitt Romney on health policy.

For now the House GOP’s election-year blueprint calls for converting Medicaid into fixed block grants to the states or a per-capita system tied to the number of beneficiaries in a state, and how sick they are.

Republicans say either option would allow governors to implement Medicaid as they see fit, resulting in a more efficient program.

Democrats, however, say both models are designed to slash federal spending, so states will be forced to slash benefits or enrollment, undercutting Mr. Trump’s campaign vow to leave entitlements alone.

“I think some of your biggest critics are going to be Republican governors on this, because I think Republican governors, and they’ll probably be [more] diplomatic than me, are going to see this as a Trojan Horse to cut spending,” Sen. Ron Wyden, Oregon Democrat, said at a confirmation hearing for Rep. Tom Price, Mr. Trump’s pick to lead the Health and Human Services Department.

Kellyanne Conway, a senior counselor to Mr. Trump, confirmed in an interview with “Face the Nation” on CBS on Sunday that the administration is eyeing block grants for Medicaid, though Wednesday’s study suggested that rolling back the expansion could upset a core bloc of Trump supporters — Southern whites.

In Louisiana, which expanded in mid-2016, white respondents who earned 138 percent of poverty or less were evenly split over Obamacare’s impact on them, while the share of whites in Arkansas and Kentucky reporting a benefit continued to “significantly exceed” this reporting harm.

“Ideology has undoubtedly played a large role in states’ decisions about whether to expand Medicaid, but it may not be the sole determinant of who ends up supporting the expansion’s repeal,” the study said.

Some Senate Republicans are reaching for a Solomonic solution.

Sens. Bill Cassidy of Louisiana and Susan M. Collins of Maine recently offered a bill that would empower states to keep Obamacare, including Medicaid expansion, adopt GOP reforms with 95 percent of the federal funding they would have received under the 2010 law or strike out on their own with no federal assistance.

Avik Roy, a conservative health policy adviser, said there are “no easy answers to anything health care, but the new Cassidy-Collins plan will no doubt appeal to the Kasichs of the world, because it allows those who like their Obamacare to keep their Obamacare, while allowing other states to opt out.”

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