Former Governor and Senate candidate Tim Kaine held a discussion with Northern Virginia women at the Dulles Marriott on October 16, 2012. (Susan Biddle/For The Washington Post)

(Editor’s note: A previous version of this story incorrectly stated the name of a group that endorsed U.S. Senate candidate Timothy M. Kaine. The group is The Feminist Majority PAC.)

George Allen and Timothy M. Kaine played to their respective strengths at dueling Northern Virginia events Tuesday, rallying their supporters in one of the country’s most hotly contested U.S. Senate races.

Three weeks before Election Day, the former Virginia governors spent Tuesday afternoon pursuing distinct constituencies: Kaine (D) courted female voters, while Allen (R) held a round-table meeting with defense contractors who are concerned about looming federal budget cuts.

At a hotel in Dulles, Kaine picked up the formal backing of the National Organization for Women PAC and the Feminist Majority Foundation, as officials from both groups urged a friendly audience to rally around the Democrat.

“This could be the deciding vote in the Senate,” said foundation President Eleanor Smeal. “I know we shouldn’t really sleep for the next three weeks.”

Kaine made clear that he needs the support of women to win, predicting female voters might turn out in even greater numbers than they did in 2008. “I think the big-picture story of the 2012 election is going to be the role of women,” he said.

Democrats are depending on energized support from Virginia women following a series of state and national controversies regarding abortion rights — including a bill in Richmond that would have required women to undergo ultrasounds before abortions and a “personhood” measure that would proclaim that life begins at conception.

A Washington Post poll released last month gave Kaine a 14-point lead among female voters, and more recent surveys have also shown the Democrat with solid advantages among women.

After the first presidential debate, some surveys have shown Republican nominee Mitt Romney (R) closing the gap with President Obama among women voters. Asked Tuesday whether he was seeing that trend in Virginia, Kaine said: “I haven’t seen it yet, though I will say, as I get to the end I don’t really spend a lot of time looking at cross-tabs. I kind of look at polls always as snapshots.”

At Tuesday’s event, Kaine accused Allen of seeking to downplay the importance of issues such as abortion and contraception. “These are not little divisive social issues that we can just brush aside,” Kaine said.

Allen’s campaign has frequently said that it believes women are most concerned about the economy and jobs, and that they would gravitate toward the Republican and away from a Kaine, a supporter of the Obama administration’s economic policies.

“The number one issue on the minds of women is jobs, despite Democrats’ attempts to play the gender card this election,” state Sen. Jill Holtzman Vogel (R-Fauquier) said in a statement released by the Virginia Republican Party.

A few hours after Kaine’s event ended, Allen sat at a conference table in a Rosslyn high-rise to hear the concerns of government contractors who are worried about the impending defense cuts that could start taking place in January, barring a bipartisan agreement to stop them.

Allen has always opposed the spending deal that put the defense cuts on the table if a deficit-reduction “supercommittee” failed. Kaine backed the original agreement, as did most Republican leaders, though Kaine says he wants the two sides to strike come to an agreement to avert the cuts.

Allen told the contractors Tuesday that jobs were already being lost because of the threatened cuts. “The reality is this is already affecting businesses, particularly the smaller contractors,” said Allen, who added that the cuts showed the Obama administration was “compounding failed leadership.”

The round-table event also delved deep into the details of government contracting, from the pros and cons of issuing shorter-term contracts to the importance of streamlining the process of protesting contract awards. Allen also said he would oppose another round of base closures — a process known as “BRAC” — because they would be too disruptive and might not save any money.

Democrats have accused Allen of presenting vague and unrealistic plans for averting the proposed cuts, because he is also opposed to any tax increases.

“Governor Kaine has laid out a detailed, specific, and bipartisan plan that will avert these . . . cuts that threaten Northern Virginia and the rest of the Commonwealth, but we’ve seen no such effort from George Allen,” Del. Bob Brink (D-Arlington) said in a statement issued by the state Democratic Party.

The cuts have been the subject of a barrage of anti-Kaine ads, including a new spot from the National Republican Senatorial Committee accusing Kaine of backing reductions that would “cripple” Virginia’s economy. Kaine’s campaign denies the claim, saying the spot distorts his position on the cuts.