On paper, the idea is simple. Voters get a call, a visit or both from a volunteer who lives in their neighborhood. An unregistered resident gets help in signing up to vote. If the voter is undecided and cares most about, say, education, the campaign will make sure that voter gets e-mails about Mr. Obama’s education policies, a heads-up the next time the president is going to be addressing the topic, and maybe even a ticket to his next event in the state. If the voter begins leaning toward Mr. Obama, the campaign will encourage early voting to lock up the support.

But in reality it can be a time-consuming and trying process, as Kathryn River has learned. When Mr. Romney began in May to organize in Ohio, the bellwether state of presidential elections, Ms. River, 25, already had been calling neighbors and going door to door for Mr. Obama for six months. She enlisted her mother, Susie Burke, 49, a pub owner and former Republican, who enters data that callers and door-knockers collect.

Ms. River recalled gingerly approaching one assigned address, where a burly, bearded man was leaning on his rifle. But, she said, after her pitch she “left feeling I’d swayed him a bit.”

After more than three years of economic ups and downs and partisan brawling, the realities of governing have dimmed the Obama magic. “The excitement is still there because we’re re-electing the first African-American president,” said Jim Bennett, 57 (who, like the two dozen other volunteers here, is white). “But it just takes a little bit more this time around to get the volunteers to come out.”

Getting them out is essential to Mr. Obama. While the president’s re-election campaign is also advertising heavily — it spent $29 million on advertising in key states last month — many in both parties expect that Mr. Romney and his allies will dominate on the airwaves. But Mr. Obama, the onetime community organizer, is banking on his ability to out-organize Mr. Romney in the states that will decide the outcome.