It's a race against time for Michigan lawmakers as they work toward a state budget agreement by the Oct. 1 deadline.

Just two days after both Republicans and Democrats said negotiations weren't going well, Rep. Parker Fairbairn, R-Sault Ste. Marie, says negotiations are improving.

For months, lawmakers have been working to reach an agreement, but they missed their July 1 deadline to pass the budget.

"Back in June, we were having productive conversations. I will say one chamber walked away from the table we couldn't meet because we need all three legs of the stool to get the job done," said Fairbairn. "So we're at the point now, you know, almost October, where everyone is at the table, everyone is operating in good faith."

Lawmakers struggled to bridge the large gap in their proposals. House Republicans passed a $78.5 billion proposal, and Senate Democrats passed an $84.5 billion proposal. Earlier this week, Reps. Aragona, R-Clinton Township, and Regina Weiss, D-Oak Park, said negotiations haven't been going well, but Fairbairn says that's changed. 

"I'd say there's more good faith happening right now, a lot better conversations going on, and I think that really is making the difference," he said. 

CBS News Detroit learned there are a number of sticking points in negotiations, such as the Republican effort to tie school and road funding together and a refusal to accept certain cuts. 

"There are going to be compromises, and I believe that both sides will have to compromise," Fairbairn said. 

Fairbairn says he feels optimistic that Michigan will avoid a government shutdown. 

CBS News Detroit contacted House Speaker Matt Hall for a sit-down, but he was pulled into budget negotiations shortly before the interview.