Republicans on the U.S. Senate Judiciary Committee plan to meet privately on Thursday to gauge support for their chairman’s embattled proposal to create a $140 billion asbestos compensation fund, a key lawmaker said on Wednesday.

Chairman Arlen Specter of Pennsylvania will confer with fellow Republicans on the panel as they determine how to proceed with his proposal that has drawn bipartisan concerns, said Republican Sen. John Cornyn of Texas.

Specter has proposed a $140 billion fund to compensate victims of asbestos, a fire-retardant mineral once widely used for insulation and construction that is linked to a number of illnesses. Specter’s proposal also would cap the liability of companies paying damages.

While Congress failed last year to reach agreement on such a proposal, Cornyn told reporters, “I’m still optimistic that we will get a bill, and I must say I’m very much supportive of Senator Specter’s efforts.”

“We are going to be having a meeting on Thursday among the Republicans on the committee to poll members to see exactly where they are on the current proposal,” Cornyn said.

Specter has said he is open to changes and Cornyn, a key figure in the asbestos talks, said committee members need to tell the chairman where they stand.

“I think we owe that to Senator Specter, we owe it to our constituents, so we can make the bill something that will get a majority of support in the Senate,” Cornyn said.

One concern is that victims do not obtain money from a new compensation fund while getting relief elsewhere, such as from state workers’ compensation systems.

Cornyn said, “The goal of the bill is to terminate the current scandalous asbestos mess by creating an alternative forum, this trust fund. We don’t want to have both the trust fund and the current broken system operating.”