The union representing thousands of nurses in Worcester is pushing a ballot initiative to mandate staffing levels at Massachusetts hospitals. The Massachusetts Nurses Association, which is affiliated with nurses at UMass Memorial Medical Center and St. Vincent Hospital, has long pushed for limits on the number of patients assigned to nurses during a shift. Staffing levels were at the heart of a contract dispute between UMass Memorial and its nurses this spring. Nurses at the hospital's University Campus nearly went on strike before coming to a last-minute deal that included higher staffing levels in exchange for lower pay raises.