FRANKFORT, Ky. (AP) — After weeks of struggling to win over some reluctant lawmakers, Kentucky Gov. Matt Bevin’s team is confident that enough votes have been rounded up to pass his pension-relief proposal in a special legislative session, a key Bevin aide said Wednesday.

“I believe the support exists in both the House and the Senate to get this bill passed,” Bryan Sunderland, the governor’s deputy chief of staff and his key liaison with lawmakers, said in a phone interview. “I think legislators have come to realize that this is a solid proposal.”

Now it’s a matter of timing for Bevin in deciding when to bring lawmakers back to the state Capitol to take up his measure, he said. The proposal would replace a bill that the Republican governor vetoed in April after the GOP-dominated legislature had ended its regular session.

“Really it’s more of a scheduling issue than a support issue,” Sunderland said.

Bevin’s proposal aims to provide relief for regional universities as well as county health departments, rape crisis centers and many other quasi-governmental agencies that face surging pension costs starting next month.

The Courier Journal first reported that Bevin’s team believes it has secured the votes need to pass the measure.

The Bevin administration’s goal is to pass the replacement measure as soon as possible, but getting it done in June would be “very ambitious,” Sunderland said. In his talks with top lawmakers, the governor has been “looking at July dates at this point,” he said.

Besides the complexities of the pension issue, another complication for Bevin has been trying to schedule a special session amid lawmakers’ long-planned vacations. Some top lawmakers have said the vote count was fluid, depending on which lawmakers would be absent in certain weeks because of vacations.

Unless action is taken, the regional universities and quasi-public agencies face ballooning pension costs starting July 1. State leaders worry that inaction would strain the quasi-public agencies and lead to some bankruptcies, elimination of staff and loss of critical services for Kentuckians.

Even if the special session doesn’t convene until sometime in July, Bevin’s administration is confident the action would still come soon enough to spare the agencies from financially crippling pension payments, Sunderland said.

“It can still get fixed,” he said.

Bevin’s proposal allows the agencies to stay with the Kentucky Retirement Systems at full cost; leave the retirement system by paying a lump sum equal to future projected benefits payments; or buy their way out in installment payments over 30 years. It extends a freeze on pension costs for another year for the regional universities and quasi-public agencies.

Bevin recently agreed to a handful of changes to his proposal in hopes of breaking the gridlock.

One key change pushed back the deadline for affected agencies to decide until next April 30, after the conclusion of next year’s legislative session. That would give lawmakers time to make changes to deal with any issues that might come up.

No other changes have been made to the bill since then, Sunderland said Wednesday.

Soon after the changes surfaced, some lawmakers remained skeptical of the proposal because they wanted a provision ensuring that certain employees in the affected agencies would have the option to keep their current benefits, House leaders said recently.

Bevin is wrangling with the pension issue as he seeks reelection this year. The governor is being challenged by his political nemesis , Democratic Attorney General Andy Beshear, in the November election.

This post has been updated.