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The issue already is popping up in multiple Senate races, including in Ohio, Nevada and Michigan, as Democratic candidates seek to push the issue. In Virginia, former Gov. Tim Kaine, the Democrats’ likely Senate nominee this year, has sent several emails urging supporters to sign a petition pushing the legislation.

“This one is a no-brainer, and I’m stunned that it’s even the least bit controversial,” Mr. Kaine said. “Of course women deserve equal pay for equal work. It’s time that we moved beyond these tired social divisions, and I’m asking for your help to make a difference.”

Former Sen. George Allen, the front-runner for the Republican nod in the race, has not taken a stand on the legislation.

“It’s unfortunate that Washington is playing politics — there is no question George Allen supports pay equality for women,” Allen spokeswoman Emily Davis said.