President Barack Obama and Hill Democrats coordinated a public relations push Monday for a pay equity bill that their allies hope will be a potent weapon against Mitt Romney.

Democrats held three conference calls to push for the bill ahead of a Senate vote today, including one featuring a brief appearance by Obama.

“We’ve got to understand this is more than just about fairness,” Obama said. “Women are the breadwinners for a lot of families, and if they’re making less than men do for the same work, families are going to have to get by for less money for child care and tuition and rent, small businesses have fewer customers. Everybody suffers.”

Democrats have used the bill to beat up Republicans as part of their “war on women” charge. They say the 2009 Lilly Ledbetter Fair Pay Act that Obama has been touting for three years doesn’t go far enough and the new bill is needed to allow workers to share salary information without threat of retribution from their employers. It also would put employers at risk of punitive damages in addition to back pay if they discriminate.

Ostensibly, the push is aimed at persuading Republicans not to filibuster the bill, but that’s a tall order. For Republicans, the push — coming years after Obama first backed the legislation — is less about pay equity and more about presidential job security. They privately dismiss the effort as another “show vote” that would be a boon to trial lawyers. And so far there’s little evidence that the Senate’s Republican women will abandon their leadership the way they did on the Violence Against Women Act. A coalition of business groups including the U.S. Chamber of Commerce has also strongly opposed the legislation.

Senate Majority Leader Harry Reid didn’t sound like he expected to win the 60 votes needed to move the bill forward.

“No woman working to support herself or her family should be paid less than her male counterparts,” the Nevada Democrat said on the Senate floor. “Yet Republicans are filibustering the Paycheck Fairness Act — legislation that would help even the playing field for women in the workforce. … It appears Republicans will wind up on the wrong side of this issue as well, sending the message to little girls across the country that their work is less valuable because they happened to be born female,” he continued.

The Romney camp, meanwhile, emailed a statement endorsing the general idea of pay equity.

“Of course Governor Romney supports pay equity for women,” campaign spokeswoman Amanda Henneberg said. But “in order to have pay equity, women need to have jobs, and they have been getting crushed in this anemic Obama economy, losing far more jobs than men. As president, Mitt Romney will create a pro-jobs business climate that will put all Americans back to work.”

On the conference calls, however, there was a repeated push for the GOP presidential nominee to endorse the bill itself, not just the topic.

“Mitt Romney and Republican candidates across the country need to stand up and say whether they will support this effort to address the serious financial challenges facing women and families,” Rep. Rosa DeLauro (D-Conn.) said on an Americans United for Change conference call.

“I’d make a $10,000 bet that Mitt Romney won’t say where he stands on fair pay because he opposes it,” EMILY’s List President Stephanie Schriock said. She said Romney knows his position is a loser with voters “so he’s choosing not to tell us where he stands.”

She also promised to let women know “who’s fought for them and who’s on the wrong side of history” heading into November.

On another call, Senate Democratic Conference Vice Chairman Charles Schumer (N.Y.) urged Romney to endorse the bill, before handing the call over to senior Obama adviser Valerie Jarrett.

“We’re committed to the basic idea that equal pay for equal work is not a luxury, it is a necessity,” she said. “We know that we’re in for a fight, but it’s a fight we can win as long as we all work together.”

Jarrett dismissed a question about the possibility of Obama issuing an executive order imposing the law’s requirements on government contractors.

“Our efforts right now are devoted to getting this act passed,” she said. “There is no interest right now in talking about a fallback.”

Sen. Barbara Mikulski, who has led the charge for the bill, said “the rational argument and the emotional argument is on our side.” The Maryland Democrat said the question is whether there will be flexibility for “moderate-thinking, fair-minded Republicans” to vote for it.

Mikulski said there have been discussions with Republicans urging them to back the bill, but she said those were confidential. Democrats wanted to pass the bill in the first two years of the Obama administration, but that effort fell short when they lost their 60-vote supermajority in early 2010, Mikulski said.