(Bloomberg) -- Senate Republicans are expressing awillingness to consider a bipartisan approach to strengtheningthe individual insurance market underObamacare, even as President Donald Trump is deciding whetherto end payments for it.

Senate Majority Leader Mitch McConnell said on Saturday he’d beopen to the attempt, which follows the collapse of Republicanefforts to repeal and replace the Affordable Care Act, according tothe Associated Press. Republican Senator Thom Tillis said he’d beobligated to consider it.

“We have got a destabilized market where insurance rates aregoing to go up 20, 30, 40 percent next year,” Tillis of NorthCarolina said on ABC’s “This Week” on Sunday. “Anything that we cando to prevent that and the damage that that will have on people whoneed health care I think is something I have to look at.”

The Senate health committee will begin bipartisan hearings inearly September on stabilizing and strengthening the AffordableCare Act’s individual insurance market, Republican Chairman LamarAlexander of Tennessee and top Democrat Patty Murray of Washingtonsaid in a joint statement on Aug. 1.

While saying he was open to a bipartisan plan for subsidies,McConnell also said on Saturday there was “still a chance” toaddress a repeal and replacement of Obamacare -- but that it wasquickly becoming unlikely, according to the AP.

Obamacare First

Trump has also tweeted to his 35.2 million followers thatsenators, who are away from Washington for their summer recess,shouldn’t vote on anything else until they’ve completed the effortto revamp President Barack Obama’s signature health law.

Health and Human Services Secretary Tom Price said July 30 that“no decision’s been made” on whether to continue key subsidiesunder the law to health-insurance companies, but that theadministration’s job is “to follow the law of the land.”

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The payments, called cost-sharing reductions, help insurersoffset health-care costs for low-income Americans. Trump hasrepeatedly suggested ending the payments as bargaining tactic tobring Democrats to the negotiating table.

The next payment is due on Aug. 21.

“The cost-sharing reductions over time need to be eliminated,”Tillis said. “But we can’t just all of the sudden pull the rug outfrom underneath an industry that has had this in place for aboutseven years.”

Need Bipartisanship

Appearing together on CBS’s “Face the Nation” on SundayRepublican Governor John Kasich of Ohio and Democratic GovernorJohn Hickenlooper of Colorado said both parties should work to finda solution.

“Republicans are going to have to admit that there is a group ofpeople out there who will need help,” Kasich said.

“I think we’ll be surprised at the number of senators that arewilling to kind of step back and say, ‘All right. Let’s roll up oursleeves, and work on a bipartisan basis, and see how far we cango,”’ Hickenlooper said.

Republican Senator Ron Johnson of Wisconsin said “we do need tostabilize those markets” but urged his colleagues to move on toother priorities.

“I really do think we probably ought to turn our attention todebt ceiling and funding the government and tax cuts until we canreally get all the parties together,” Johnson said on CNN’s “Stateof the Union” on Sunday.