Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellObama calls on Senate not to fill Ginsburg's vacancy until after election Planned Parenthood: 'The fate of our rights' depends on Ginsburg replacement Progressive group to spend M in ad campaign on Supreme Court vacancy MORE (R-Ky.) is signaling that he's open to a bipartisan deal on key payments to health insurance companies, but warning any agreement needs to include "real reforms."

“If the Democrats are willing to support some real reforms, rather than just an insurance company bailout, I would be willing to take a look at it,” McConnell told reporters in Kentucky ahead of the annual Fancy Farm Picnic over the weekend.

He added that while there is "still a chance" the Senate will take back up its ObamaCare repeal and replace effort, Sens. Lamar Alexander Andrew (Lamar) Lamar AlexanderChamber of Commerce endorses McSally for reelection Trump health officials grilled over reports of politics in COVID-19 response Now is the time to renew our focus on students and their futures MORE (R-Tenn.) and Patty Murray Patricia (Patty) Lynn MurrayTrump health officials grilled over reports of politics in COVID-19 response CDC director pushes back on Caputo claim of 'resistance unit' at agency The Hill's Morning Report - Sponsored by The Air Line Pilots Association - Pence lauds Harris as 'experienced debater'; Trump, Biden diverge over debate prep MORE (D-Wash.) are also working on "some kind of bipartisan approach" to stabilize the individual insurance market.

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Several Republican senators, including GOP Sen. Lindsey Graham Lindsey Olin GrahamSenate Republicans face tough decision on replacing Ginsburg Democratic senator calls for eliminating filibuster, expanding Supreme Court if GOP fills vacancy What Senate Republicans have said about election-year Supreme Court vacancies MORE (S.C.), are expected to use the August recess to try work on their ObamaCare replacement bills.

But Alexander and Murray announced last week they would hold a series of bipartisan Health Committee hearings next month.

Their goal is to craft a insurance stabilization bill by mid-September that is expected to include money for ObamaCare's cost-sharing reduction payments, which President Trump has threatened to cut off.

"Our goal is to have hearings and come to a consensus by mid-September that would stabilize that individual market and make policies affordable for people like the 350,000 Tennesseans," Alexander told The New York Times.

Alexander and Murray could face an uphill battle to getting any legislation to Trump's desk. First, they'll need to clear it through their politically diverse committee, which includes Republican Sens. Rand Paul Randal (Rand) Howard PaulSecond GOP senator to quarantine after exposure to coronavirus GOP senator to quarantine after coronavirus exposure The Hill's Morning Report - Sponsored by National Industries for the Blind - Trump seeks to flip 'Rage' narrative; Dems block COVID-19 bill MORE (Ky.) and Susan Collins Susan Margaret CollinsSenate Republicans face tough decision on replacing Ginsburg Democratic senator calls for eliminating filibuster, expanding Supreme Court if GOP fills vacancy What Senate Republicans have said about election-year Supreme Court vacancies MORE (Maine), as well as Democratic Sen. Elizabeth Warren Elizabeth WarrenBiden's fiscal program: What is the likely market impact? Warren, Schumer introduce plan for next president to cancel ,000 in student debt The Hill's 12:30 Report - Presented by Facebook - Don't expect a government check anytime soon MORE (Mass.) and Independent Sen. Bernie Sanders Bernie SandersKenosha will be a good bellwether in 2020 Biden's fiscal program: What is the likely market impact? McConnell accuses Democrats of sowing division by 'downplaying progress' on election security MORE (Vt.).

Even if a bill were to pass the Senate, it would likely face greater resistance in the House, where conservatives and outside groups are deeply opposed to what they view as a "bailout" for ObamaCare.

But Alexander added in his comments to The Times that he thinks lawmakers will be able to find a deal, which he said could include narrow fixes.

"I think we can do that. I think Democrats and Republicans agree that that market where 6 percent of Americans get their insurance is in trouble and we need to fix it," he said.