CHICAGO (CBS) — Chicago aldermen were poised to approve Mayor Rahm Emanuel’s proposal to raise the city’s minimum wage to $13 an hour by 2019.

The City Council Committee on Workforce Development on Monday backed the mayor’s proposed ordinance Monday afternoon, and sent it to the full City Council for a vote on Tuesday at a special meeting specifically for the minimum wage plan.

The mayor’s plan would gradually increase the minimum wage each July through 2019, when it would be raised to $13 an hour. The ordinance also would raise the minimum wage each year after that, at a rate equal to the rise in the Consumer Price Index.

The Raise Chicago Coalition, which has pushed for a $15-an-hour minimum wage, wasn’t giving up their fight to go further than Emanuel has proposed. They called the mayor’s ordinance a good start. Ald. John Arena (45th) said it’s just not enough of an increase over the current $8.25 an hour.

“So we need to work over the next couple of hours, the next couple of days, to make sure that we get the best deal that we can get for Chicago’s workers; and continue that fight, both here and down in Springfield,” he said.

Business groups have said a higher minimum wage will hurt retailers, restaurant owners, and others.

The National Restaurant Association warned Emanuel’s proposal for a $13-an-hour minimum wage would eliminate 11,600 jobs in Chicago.

State lawmakers were set to return to Springfield on Tuesday for a three-day veto session, and could vote on proposed legislation to raise the state’s minimum wage to $11 per hour by 2017. Some lawmakers have said they want to limit Chicago’s ability to raise the city’s minimum wage any higher than the state’s.