State Assembly Speaker Craig Coughlin said Friday he expects his house will vote in the coming months on a much-anticipated bill raising the minimum wage in New Jersey gradually to $15 an hour.

Despite broad support among Democrats who control the state Legislature for this big boost in the minimum wage, legislation has snagged on disagreements over whether certain categories of workers should be excluded.

Coughlin, D-Middlesex, said on radio station WCTC 1450-AM that he hopes to have a completed bill "in very short order" that the Assembly can vote on in December, at the earliest.

"If it doesn't get done at the Dec. 17th voting session, then it will be done right after the new year, probably at the first voting session in January," he said. "At least that's my goal as of right now."

State Senate President Stephen Sweeney, D-Gloucester, told NJ Advance Media on Friday that Coughlin has been drafting a bill that will become the basis for negotiations between the two houses.

Sweeney is hopeful the Legislature can meet the speaker's timeline, he said.

"I'm going to work with the speaker and I expect to get it done," Sweeney said. "I think we'll get there pretty quick."

New Jersey's minimum wage is $8.60 an hour. It will rise 25 cents an hour to $8.85 on Jan. 1, based on a constitutional amendment tying annual increases to changes in the consumer price index.

Proponents of a $15 minimum wage argue those small annual bumps have not kept up with the state's high cost of living.

Someone working 40 hours per week at $8.60 an hour will earn $344 a week, or $17,888 a year.

At $8.85, that worker will earn $354 a week, or $18,408 a year.

Gov. Phil Murphy, also a Democrat, has said hiking the minimum wage is a top priority. In his January inaugural address he asked the Democrat-controlled state Legislature to send him a minimum wage bill, and he's repeated the request since.

A minimum wage bill passed by the Legislature in 2016 and vetoed by former Gov. Chris Christie, a Republican, would have moved to $15 an hour over 5 years. Coughlin said on his call-in radio show "Speak to the Speaker" that aspect of the new bill "is still in the works."

"We're going to work toward a $15 minimum wage," he said. "I think there is agreement among the governor, the Senate president and myself that we need to get there, because so many people in the state struggle to make ends meet and so many people have to work two or three jobs to do that."

Samantha Marcus may be reached at smarcus@njadvancemedia.com. Follow her on Twitter @samanthamarcus. Find NJ.com Politics on Facebook.