ST. PAUL (AP) — Amid rising labor union pressure, public negotiations resumed Tuesday on efforts to raise Minnesota’s nation-trailing minimum wage for the first time in almost a decade.

A House-Senate conference committee held an 11-minute hearing, its first public session since early March. The six lawmakers on the panel, all Democrats, looked out over a room packed with public employee union members who are part of a “Raise the Wage” coalition demanding a deal get done after last year’s deadlock. The House team made an offer that senators said they needed time to review.

Hours earlier, the union members voiced frustration with their typical Democratic allies for not moving more quickly to resolve the issue when they control the legislative and executive branches. At a boisterous rally, a state chapter of the American Federation of State, County and Municipal Employees booed mention of hesitancy within the state Senate to pass a bill that pushes the wage up to $9.50 per hour and automatically links future bumps to inflation.

Minnesota’s minimum wage for all but the smallest of businesses is $6.15 per hour, though many workers automatically receive the higher federal minimum of $7.25 per hour. Some workers such as baby sitters, taxi drivers, nonprofit volunteers and others are exempt from the minimum wage. The Minnesota wage hasn’t gone up since 2005.

Of the 45 states with a minimum wage, Minnesota joins only Arkansas, Georgia and Wyoming with a wage lower than the federal rate. All of Minnesota’s neighbors are at $7.25 per hour.

Last year, the Senate approved a bill gradually raising Minnesota’s minimum hourly wage to $7.75. The House-adopted plan lifted it to $9.50 per hour, phased in over time and attached the automatic increasing feature known as indexing. The session ended without a deal.

Early this session, the Senate budged on its position and offered to push the wage to $9.50 by 2016. But key senators said they were eight to 10 votes short of what it would take to pass a bill with the automatic inflator later on.

On Tuesday, Rep. Ryan Winkler came back with a new variation that would reach the $9.50 threshold for businesses with more than $500,000 a year in gross sales, with a lower top-end minimum wage for smaller businesses and for companies training in new hires. Beginning in 2017, the floor wages in all three tiers would climb by an inflationary amount as long as it doesn’t exceed a hard cap.

“By putting $9.50 in and indexing it to the cost of living as it goes up, we make sure the floor for workers’ pay goes up with it,” Winkler said.

Sen. Chris Eaton, DFL-Brooklyn Center, promised a response after consulting with the rest of the Senate Democratic majority on Wednesday night.

Sen. Jeffrey Hayden, DFL-Minneapolis, said even though some of his colleagues have been reluctant to budge so far, he doesn’t believe they’ve locked into opposition.

“Things change around here and they’re pretty fluid,” Hayden said. “It was clear we didn’t have 34 votes for the last proposal so I’m trying to see if we can get 34 votes for this one or come back with a proposal that’s something they can vote for.”

Minneapolis restaurant owner Naomi Williamson cautioned lawmakers about pushing the wage up too high too fast, particularly for servers who also qualify for tips.

“People’s jobs are going to be cut back and those are the server jobs,” she said.

Lawmakers have until mid-May to finish their session. None of the wage changes in any of the proposals would take effect until Aug. 1.