Gov. Dannel P. Malloy said Tuesday he’s hoping for a new concession agreement with state employee union negotiators within the next 24 to 48 hours.

The governor ate lunch at a Southbury bed and breakfast, visiting with members of the Litchfield Hills Bed and Breakfast Association as part of his jobs tour. There he told B&B owner and Southbury first selectman candidate Ed Edelson he expects an agreement on Tuesday or Wednesday.

Malloy knocked on the wooden dinner table as he told the group he hopes to have the “budget mess,” a $1.6 billion shortfall for the next biennium, cleared up within the next two weeks.

Monday’s news that union leadership voted to change their bylaws to make passing an agreement easier, offers a road to avoiding layoffs, he said. The new language changes the number of unions that it needs to ratify the agreement from 14 to 8 and reduces the threshold of voting members from 80 to 50 percent.

“I think it’s in everyone’s best interest that we get to that point. No one wants to see the diminution of services that would otherwise be required or the loss of jobs that would otherwise be required to place the budget in balance,” he said. But the budget will be in balance one way or another, he added.

If an agreement is reached and ratified, the governor said employees who have already been laid off stand a good chance of getting their jobs back.

“I think in all probability the vast bulk those layoffs would go away, with respect to members of the unions,” he said.

Some people will likely still lose their jobs. Malloy said he has planned the elimination of some management jobs as a result of agency consolidations.

He speculated a new agreement will look much like the original agreement, except the new agreement will have to address the fact that on July 1, about 40,000 state employees got raises.

“We got to figure out a way to get that money back,” he said.

Worker paychecks will reflect those raises on July 29. Malloy said so far they don’t amount to a whole lot of money but as time goes on they will begin to add up to a substantial number. Office of Policy and Management Secretary Ben Barnes said the raises amount to somewhere around $5 million per pay period. But he noted the cost of the first pay period may be a little higher due to differences in the contracts of some state employees who get top step bonuses instead of raises.

“If we had an agreement in place in early August then you’re probably talking about having to claw back one or two pay periods, that’s all,” Malloy said.

Matt O’Connor, spokesman for the State Employee Bargaining Agent Coalition, said union negotiators have been in talks with representatives of the administration. He declined to speculate on when an agreement may be reached, saying doing so could handicap the outcome. But unions understand the time constraints and will continue to work until a deal has been reached, he said.

“We understand the clock has stopped ticking. The old grandfather clock is broken. You can crank it as many times as you want but we’re out of time,” he said.

Malloy spent about an hour with the innkeepers, eating chicken and pie while discussing tourism and ways to brand the state. When it was all over Edelson asked him to film a quick endorsement for his campaign. The governor agreed and said he’d even put his jacket back on for it.

“Select Ed,” he said into Edelson’s smartphone. “He’s the best.”