Senate Democrats say lawmakers are on the cusp of a bipartisan health care deal aimed at stabilizing the individual insurance market over the next two years.

Sens. Lamar Alexander and Patty Murray, the chairman and ranking member of the Health, Education, Labor and Pensions Committee, resumed talks on a narrow stabilization package after Republicans decided not to vote this week on a proposal to overhaul the 2010 health care law.

Senate Minority Leader Charles E. Schumer of New York said Thursday on the Senate floor that the two were “on the verge” of an agreement.

A senior Democratic aide said the concessions that Murray had made before Republicans stopped the negotiations earlier this month were still on the table, so it made sense that both sides were close to a deal.

Alexander, though, said the two were still vetting the issue with their colleagues.

“It’s not a matter of just whether Sen. Murray and I agree. It’s whether we can find a consensus among Republicans and Democrats that we believe can be enacted into a result,” the Tennessee Republican said. “She and I might be able to come to an agreement. But that won’t do the job.”

The panel held a series of hearings this month on ways to stabilize the individual insurance market. Alexander has described a package that would include an appropriation for the law’s disputed cost-sharing payments, additional flexibility for states seeking waivers from health law requirements and perhaps allowances for more people to buy basic catastrophic health plans. He’s cautioned that any plan needs to be able to win the support of Republicans in Congress and the White House.

Repeal strategy

Meanwhile, Republican Sens. Lindsey Graham of South Carolina and Bill Cassidy of Louisiana, who crafted the replacement plan that was abandoned for now, met Thursday with President Donald Trump.

7 Years of Republican Efforts to Repeal and Replace Obamacare

Graham said after the meeting that they are planning to address the concerns of senators who had not backed the plan since it did not move through regular congressional order.

The top target seemed to be John McCain of Arizona, who said he supported the concepts in the bill but preferred to see committee action and a full Congressional Budget Office estimate before a floor vote.

“I really do believe we’ll have the votes with a better process,” Graham said. “The truth of the matter is it’s not a substantive issue, it’s a process issue … Senator McCain’s concerns about the process were shared by many people. Most Republicans prefer block grants over Washington control. So I’m highly confident that we’re going to get the votes with a new process, and that’s what I think the president is trying to say.”

While Senate Republicans are resigned to the fact that they won’t roll back the act before the fiscal 2017 budget reconciliation procedures expire Saturday, GOP leaders say they’ll keep working on the issue while writing a tax overhaul, with plans to return to health care before the elections next year.

Graham added that Trump mentioned Alexander and Murray’s work to strike a stabilization measure, and that Trump appeared to want changes to the law if he was going to continue making the cost-sharing subsidy payments.

“I do believe the president is really practical,” Graham said. “I came away thinking that the president is not going to continue this practice forever. He’s not going to keep throwing good money after bad. But if he does make these payments, even short-term, he wants to see some reforms.”