"It's getting close unless something falls apart," Beebe said.
Members of the legislature late Monday indicated the session would begin on June 30.
A spokesperson for the governor's office says Beebe would likely make a determination on Tuesday for which topics would make the special session agenda.
A legislative task force has come up with an estimated $40-$50 million in savings for the Public School Employees insurance plan through the elimination of part-time employees and spouses who have other options for health coverage.
Beebe proposes moving $6 million from the state budget to help open 600 existing beds to help offset overcrowding at county jails across the state.
"We can provide some relief for the counties," Beebe says. "If the counties are running 2400 to 2500 state prisoners then obviously 600 doesn't solve that problem but 600 solves a lot of it."
A simple majority is required to pass legislation, but Beebe has maintained he wants 60-percent support in both chambers before deciding to call a session.
"We're there in both houses for those two issues," Beebe says.
The Senate would like to add the banning of lottery monitor games to the special session call, but support late Monday for the idea was not materializing in the House.
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