Unions are hoping midterm election wins by more than 700 members across the country will translate into a wave of labor-friendly state and federal legislation.

Organized labor mounted one of its largest political campaigning efforts before the Nov. 6 election. According to the AFL-CIO, union members knocked on more than 2.3 million doors, worksites saw 5 million political flyers pass through the hands of employees, and voters opened their mailboxes to more than 12 million AFL-CIO mailers.

That helped get...