The union has been negotiating with Luxembourg-based ArcelorMittal since April over a new labor contract that would cover more than 14,000 workers and tens of thousands of retirees. The current contract expires Monday.
On Tuesday, the union distributed a notice to workers at 14 plants operated by ArcelorMittal saying there had been a lack of progress in the talks and asking for the authority to call a strike if the negotiations fail.
ArcelorMittal said it remains committed to working with the union to reach a settlement before Monday.
The workers cast votes in meetings throughout the day, according to Tony Montana, a USW spokesman participating in the talks.
They included employees at facilities in Indiana, Ohio, Pennsylvania, New York, South Carolina, West Virginia and Minnesota.
Among the contentious issues are premiums for retiree health care, company contributions to a trust fund for health care, employee incentives, a profit-sharing agreement and capital investments for aging facilities.
Bill Steers, an ArcelorMittal spokesman, said the talks continued with frequent meetings throughout the day in Pittsburgh.
"The company and union have reached tentative agreements on many of the outstanding issues, but continue negotiating on a handful of topics," he said in an e-mail message.
The United Steelworkers have cited a tentative four-year deal reached earlier this month with United States Steel Corp covering 16,000 workers at domestic flat-rolled and iron ore mining plants, and tubular operations in Ohio and Alabama.
ArcelorMittal employs more than 320,000 people in more than 60 countries. That includes about 18,000 employees at 17 facilities in the United States.
The company produces a tenth of the world's steel. It has said it plans to increase shipments by more than a fifth by 2012 due to robust global demand.