HARTFORD -- The union representing Connecticut State Police, one of four to reject a $1.6 billion concessions package, has asked Gov. Dannel P. Malloy's administration to engage in separate talks for givebacks.

The request comes as leaders of the 15-union State Employees Bargaining Agent Coalition continue to search for a way to salvage the giveback deal and avoid thousands of layoffs over the summer. One labor source said SEBAC leadership may change its bylaws to allow the 26 of 34 bargaining units that supported the health care and pension givebacks to accept them, leaving the eight in opposition operating under the status quo.

But, the source noted, SEBAC leaders would be unable to act on any proposed rule changes until 30 days from their being put on the table. And Malloy on Thursday set a deadline of Aug. 31 for SEBAC to ratify the concessions.

Under what many say are exceptionally tough ratification standards, 14 SEBAC unions had to back the $1.6 billion deal their negotiators reached in the spring with Malloy, a Democrat elected last November with help from organized labor.

At least 80 percent of SEBAC's voting members had to cast "yes" ballots.

When voting ended last weekend, four unions had balked at the deal, even though 57 percent of members overall embraced it.

That left Malloy and the General Assembly scrambling to plug the $1.6 billion hole in the new two-year budget before the start of the fiscal year Friday. The Legislature meets in special session Thursday to consider the governor's plan to eliminate 6,500 jobs -- including about 5,500 by layoffs -- and to grant him extraordinary powers to privatize services and enact deep service cuts.

SEBAC's leadership on Monday decided to indefinitely delay finalizing the vote, arguing 57 percent of its members -- a solid majority -- wanted the concessions.

"We're respectful of the voting process, but we have to figure out what we can do to be part of a positive solution moving forward," SEBAC spokesman Larry Dorman said Wednesday. "We can't simply pack our bags and go home with all of these potential layoffs, service cuts and devastation waiting around the corner."

Speculation that SEBAC officials may seek re-votes or alter ratification rules has led to dissension.

"People are talking about hiring labor attorneys and organizing," Gene Mauro, a Danbury-based probation officer who opposed the givebacks, said. "This is just a mess. The vote went down by their (SEBAC's) rules. If it had gone their way, would they have allowed us to have a re-vote? You lost something by your own rules."

But Rob Ramonas, a correctional head nurse working in New Haven who voted "yes," said, "To get 14 out of 15 unions to agree on anything, even if it's the sky is blue, is a difficult benchmark to reach. I think that, fundamentally, it's wrong to change the rules after the game. (But) I think it's in our long-term best interests to approve this thing."

Lois McCracken, a librarian at Housatonic Community College in Bridgeport, supported the concessions. She said she believes some workers who opposed them, like the state police, did so because they are considered immune from layoffs.

"I've lost faith in this whole SEBAC unit when we don't all have the same stakes," McCracken said.

Andrew Matthews, president of the state police union, in a letter sent this week to Malloy and obtained by Hearst Connecticut Media Group, argued his members face unique professional challenges.

"In order to continue to be a part of the (budget) solution and to ensure a successful conclusion to the process and the overall agreement between SEBAC and the administration, the Connecticut State Police Union is respectfully and formally requesting to bargain separately," Matthews wrote.

Malloy's office declined comment. Dorman did as well, saying it is an internal SEBAC matter.

Michael Merrill, dean of the Harry Van Arsdale Jr. Center for Labor Studies at Empire State College in New York, said he did not have an issue with SEBAC considering bylaw changes to allow the concessions to move forward.

"Why should the minority determine the outcome?" he said. Merrill said SEBAC needs to prove to anti-union Republican governors like New Jersey's Chris Christie that Malloy's efforts to collaborate with labor are not a failure.

"If the Connecticut model doesn't work, the advocates of the New Jersey model are going to crow," Merrill said.