WASHINGTON — Top Senate Republicans may try preserving a tax boost on high earners enacted by President Barack Obama in a bid to woo party moderates and rescue their sputtering push to repeal his health care overhaul.

The break from dogma by a party that has long reviled tax boosts — and most things achieved by Obama — underscores Senate Majority Leader Mitch McConnell’s feverish effort to yank one of his and President Donald Trump’s foremost priorities from the brink of defeat.

The money from the tax boost would instead be used to bolster proposed health care subsidies for lower-income people.

The change, proposed by Sen. Bob Corker, R-Tenn., would give a more populist flavor to the bill. The nonpartisan Congressional Budget Office says that as the legislation now is written, it would boost out-of-pocket costs for many poor consumers and produce 22 million uninsured people while cutting around $700 billion in taxes over a decade — largely for richer people and the health care industry.

“You’re increasing the burden on lower-income citizens and obviously alleviating the burden on the wealthy. That is not an equation that works,” Corker said. He said he was “very confident” that leaders would address the issue in the updated bill.

[READ MORE: Most Americans disapprove of GOP’s treatment of health care]

Top Republicans also considered an amendment pushed by conservatives to let insurers offer plans with low premiums and scant benefits. To do so, a company would also have to sell a policy that abides by the consumer-friendly coverage requirements in Obama’s 2010 statute, which the GOP is struggling to repeal.

Both proposals were encountering internal Republican opposition, and it was uncertain either would survive. But the effort underscored how McConnell, R-Ky., needed to mollify both wings of his divided party to rescue his health care legislation, which he wrote secretly but has floundered.

McConnell postponed a vote on an initial version Tuesday because of opposition from conservatives and moderates alike. By this week’s end, he wants to nail down changes that would assure the bill’s passage after Congress’ weeklong July 4 recess. No more than two of the 52 GOP senators can oppose the measure for him to prevail, and there were no indications he’d achieved that margin as senators left town Thursday.

“We’re kind of at a stalemate right now, I’d say,” said Sen. Shelley Moore Capito, R-W.Va., who with Ohio GOP Sen. Robert Portman and others wants to forestall reductions the measure would make in Medicaid. Discussions about easing those cuts were continuing, but progress so far was “not enough for me,” said Sen. Dean Heller, R-Nev. Trump weighed in on the stalemate Friday morning, tweeting: “If Republican Senators are unable to pass what they are working on now, they should immediately REPEAL, and then REPLACE at a later date!” That’s an approach advocated by Kentucky Republican Sen. Rand Paul.

The Medicaid program for low-income and disabled people has grown dramatically in their states and others, but the Republican bill would cut it, with reductions growing over time.

The CBO says Medicaid cuts in the Senate Republican health care bill would take a 35 percent bite off the program’s projected spending by 2036.

[READ MORE: Why McConnell plans to hide health care bill’s pain until after the midterms]

Under Corker’s proposal, the bill would retain Obama’s 3.8 percent tax increase on investment income for married couples making more than $250,000 a year and individuals making more than $125,000. Keeping that increase would save $172 billion over 10 years, and moderates want to use that money to make coverage more affordable for poorer consumers.

“If it takes something like that to get our members on board to move this process forward, I think we have to consider that,” said No. 3 Senate GOP leader John Thune of South Dakota.

Conservatives said they opposed the idea, along with the chairmen of Congress’ two tax-writing committees: Senate Finance chairman Orrin Hatch, R-Utah, and House Ways and Means chairman Kevin Brady, R-Texas.

Also in play was a proposal by Sen. Ted Cruz, R-Texas, to let insurers offer skimpier policies, which conservatives say would lower premiums.

Moderates oppose that, especially if it lets insurers raise premiums on people with pre-existing medical problems. No. 2 GOP leader John Cornyn of Texas suggested the proposal might not survive because Senate rules won’t allow it on the bill.

The leader of the conservative House Freedom Caucus suggested the Senate bill would be doomed if it excluded something like Cruz’s plan or House-approved provisions letting insurers charge higher prices to people with serious diseases. Many expect the House to try for quick passage of any health care bill the Senate approves, foregoing potential problems of negotiating a bicameral compromise.

“Is failure an option? Absolutely not,” said Rep. Mark Meadows, R-N.C. “Is failure on the doorstep knocking? Absolutely. So we’ve got to make sure we don’t answer that door.”

Republicans also said party leaders agreed to add $45 billion for battling opioids abuse to their bill. They were also considering a proposal by conservatives to let people use tax-advantaged health savings accounts to pay health care premiums.

___

Associated Press writers Erica Werner, Mary Clare Jalonick, Kevin Freking and Stephen Ohlemacher contributed to this report.