Labor leaders say unions will spend $400 million in this year’s federal, state and local elections, about the same as in 2008. Predictions about spending by conservative groups — including Americans for Prosperity, Restore Our Future and Karl Rove’s American Crossroads — suggest they may together spend at least $800 million on federal elections.

But precise comparisons are difficult. According to the Center for Responsive Politics, corporate PACs and corporate employees made $2 billion in political donations during the 2008 campaign, compared with $75 million from labor unions, based on Federal Election Commission filings. The union number does not include donations that union members make to individual candidates, and includes only a small fraction of what unions spend on politics, like amounts for campaign mailings to members and for political staff members who lobby Congress, state capitals and city halls.

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The election commission’s $2 billion figure for donations from corporate PACs and employees did not include the amount that business spends on lobbyists or business’s political donations to the U.S. Chamber of Commerce.

Some conservatives raise an eyebrow over unions’ claims that they are outgunned in the money game. “I look at them saying they’re going to be outspent, and I say, I don’t know, maybe that’s the case, but it also sounds an awful lot to me like they’re trying to manage expectations,” said Seth Morgan, the Ohio director of policy for Americans for Prosperity. The group says it is opening seven offices in the state and has called more than one million Ohio voters. “Think about it: they’ve got a built-in funding mechanism after all,” Mr. Morgan said.

If labor cannot provide the counterpunch to the conservative super PACs, it is unclear whether anyone else can. Nationally, organized labor has long been viewed as having the most effective political operation for Democrats. President Obama’s victory in 2008 here in Ohio — no Republican in modern times has been able to capture the White House without winning the state — was due in no small part to labor’s get-out-the-vote push. People from union households represented 30 percent of all who voted in the state that election.

But over the past two years, unions have been diverting resources to a range of causes beyond presidential politics, including contract showdowns with companies like Caterpillar and legislative battles over a wave of state laws diminishing collective bargaining power. Still, union leaders argue that the battles over public employees’ bargaining rights in Wisconsin and elsewhere brought new momentum and vigor to union activists, who pushed successfully to repeal a Republican-backed anti-bargaining law in Ohio in a statewide referendum last November.

“What we saw in the past two years in all these state battles across the country is members coming out of the woodwork to volunteer,” said Lee Saunders, the president of the American Federation of State, County and Municipal Employees.

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Moreover, the same Supreme Court decision that permitted unlimited donations to super PACs has also in ways benefited unions. The ruling in the Citizens United case and subsequent court rulings opened the door to unlimited corporate and union contributions to political committees and made it possible to pool that money with unlimited contributions from wealthy individuals. It also allowed unions to campaign beyond their membership for the first time — to call and knock on the doors of nonunion households. As a result, unions boast that they will reach a far larger universe of voters than ever in 2012.

Here in Ohio, union leaders expect that a record number of volunteers, pressing for Mr. Obama and Senator Sherrod Brown, a Democrat and a favorite of labor, will call or knock on the doors of 2.3 million voters by Election Day, Nov. 6, double the number they reached in the last presidential race.

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“The truth is we’re never going to come remotely close to matching the money on the other side,” said Jim Lowe, a senior organizer for the A.F.L.-C.I.O. “But this allows us to reach a far wider audience.”

Labor is facing another problem: Many union members are frustrated with Mr. Obama’s performance, having hoped he would do more to reduce unemployment, push for stimulus and infrastructure spending and stand up to Congressional Republicans.

Union leaders are urging disillusioned members to back Mr. Obama anyway, telling them that Mr. Romney will lavish tax cuts on the rich, weaken unions and do little to discourage outsourcing. They insist that no one can do as much as unions to block his strategy of running up a large majority among white working-class workers, which many political experts say he needs to win.

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Ohio, which Mr. Obama won in 2008 by four percentage points, is seen as a major battlefield for the blue-collar vote. Jobs are on nearly everyone’s minds here, even as growth in the energy and auto industries has helped reduce unemployment to 7.2 percent, below the nation’s 8.3 percent rate. In July and August alone, forces on both sides of the presidential race spent $43 million on commercials in Ohio, according to Kantar Media/CMAG, with supporters of the Republicans outspending Democrats by $3 million.

Union organizers are building what they say will be a groundbreaking, high-tech update on their old-school methods of canvassing neighborhoods and calling people.

They plan “tele-town halls,” where union leaders will address thousands of people sitting in their living rooms. They have combined forces with nonlabor groups like MoveOn.org. And volunteers no longer need to go to a central phone bank to make calls; a labor-sponsored computer program lets them call from home and match Facebook friends to targeted lists of voters so that volunteers can reach out to them on social media.

In Ohio last week, though, Kim McDonald, a special education aide and union member, said she had taken part in a traditional canvass in Cleveland Heights and would do so again. “Talking to someone about issues, face to face, should definitely help assuage the commercial onslaught,” she said.

Ms. McDonald said she had 28 doors to knock on that day, and found just six people at home. In the end, she said, she thought she had swayed perhaps two voters.