Republicans on the Senate Judiciary Committee asked for further changes in a plan for a $140 billion asbestos compensation fund at a meeting to air their concerns, a key lawmaker said on Thursday.

Sen. John Cornyn of Texas told reporters afterward that he thought committee chairman Sen. Arlen Specter would “hopefully” make some modifications to the draft bill that would take asbestos injury claims out of the courts.

“It was very good and constructive. Everyone was very frank and specific about what their concerns were. But everyone remains committed to getting a bill out,” Cornyn said.

Specter, a Pennsylvania Republican, met with other members of his party on the judiciary panel in an effort to gauge support for the embattled proposal for a fund to compensate victims of asbestos. The plan has critics in both parties.

Democrats have publicly embraced the draft bill of Specter’s plan, while conservative Republicans have become more and more critical of it.

Cornyn said concerns remained over making sure the awards from the proposed fund were offset by compensation already paid under other schemes, such as through a workers’ compensation plan.

Cornyn, whom Senate Majority Leader Bill Frist has asked to work on the issue, said earlier this week that the asbestos proposal as it now stood had so little Republican support that it might not get out of the Judiciary Committee.

Specter has said he is open to changes. In addition to the questions about victims getting compensated twice, Republicans are also worried about a provision in the bill that would give up to $200,000 to smokers with lung cancer who have no evidence of asbestos disease, and provisions allowing claimants to return to court in some circumstances.

However, changes by Specter in some of these areas could alienate Democrats, who are protective of workers’ compensation rights and would prefer that the award levels in the fund were even higher. Democrats also insist that claimants should be able to return to court if the money in the fund runs out.