The union representing more than 3,000 nursing home workers in Connecticut voted this week to postpone a strike until next month.

The strike deadlines for some homes were pushed back to May 3. Deadlines for others were delayed until May 10. The union’s contract with 34 homes expired March 15.

“Absent agreements on contracts, there will be no further postponements,” wrote New England Health Care Employees Union District 1199 President Jerome Brown in a letter to Gov. M. Jodi Rell and legislative leaders. “We must set deadlines. Otherwise, the employers we deal with will not take our issues seriously.”

Contracts at 34 homes expired March 15. Workers ranging from nurses to laundry staff are covered under the contracts. Five homes have reached agreements with workers since the contract expiration. Rell and lawmakers in the General Assembly have been trying to push through a tax on the homes that would release unreleased and eligible Medicaid dollars.