A cold autumn rain was falling on thirty people standing in the parking lot of The Coffee Loft in Marlborough, a swing town in Republican-leaning central Massachusetts, as they prepared to knock on doors for Elizabeth Warren. The state Democratic Party chair, John Walsh, gave an upbeat pep talk about grassroots organizing. “You are the antidote to all the things people hate about politics,” Walsh said, in a simultaneously calm and inspiring voice. “They hate top-down politics, people yelling at each other on television and attack ads that have nothing to do with anything that matters. They can’t believe that show hasn’t been canceled already. They want to have a civil conversation about issues they care about. That’s you.”

These thirty volunteers—and thousands of others who are doing the same thing across Massachusetts every weekend—are one of three reasons Elizabeth Warren might eke out a victory against Scott Brown. Warren herself brought in a flood of volunteers. The Democratic convention activated still more. And in the last five months, the campaign, the state party and the DNC have coordinated effectively to put each one of those people quickly to work getting votes. That’s exactly what did not happen in the January 2010 special election to replace Senator Ted Kennedy, when Brown surprised everyone and won.

Warren has been ahead, albeit within the margin of error, in four out of the last five polls, with roughly 5 percent of likely voters undecided. Some of those in the middle are genuinely undecided, torn between his likability and her fiery passion to help the middle class. Others haven’t paid attention yet; they’re putting off doing their “homework” on that awful show that John Walsh says they wish were canceled. Those Marlborough volunteers trying to keep the rain off their brochures were aiming to inform the uninformed, persuade the undecideds and identify anyone who should be reminded on November 6 to vote.

The Warren campaign—in tight cooperation with the highly energized state Democratic Party—has been relentless, organized and enthusiastic. The candidate herself made more than 150 officially scheduled public appearances between June 1 and October 15, 2012—from the Revere sand sculpting festival (on a beach where, not so long ago, you had to avoid the discarded needles) to the Massachusetts Building Trades clambake in suburban Hopkinton. That doesn’t count informal drop-ins, in-house fundraisers and behind-the-scenes meetings with political figures around the state.

Her tens of thousands of volunteers are hard at work meeting everyone she can’t get to. If it’s Wednesday night, local offices have “women for Warren” phone banking; Monday nights are “men for Warren”; Saturday, Sunday and Tuesday evenings are for door-to-door canvassing. Walsh told me that volunteers have knocked on more than 850,000 doors—an astonishing proportion in a state of just under 6.6 million, especially if, as Walsh claims, people who’ve talked to canvassers will mention those conversations to five other people. The unions are working hard to get their members to vote against Brown’s record, despite the fact that the union guys feel more comfortable with him than with “the professor.” Her television commercials are hitting the right points and feature the right local surrogates. Endorsers like the independent mayor of Lowell, site of dangerous postindustrial urban decay, and five-term Boston mayor Tom Menino—both of whom could easily have sat out the race—are putting their neighborhood operations to work for Warren.

Leafy Marlborough is a former mill town that has become a pretty suburb. Some of its residents live in its split-levels and saltbox Capes and work in nearby office parks, reaping mid-Massachusetts’ high tech and new-business prosperity. Ohers are struggling, keeping their yards neat around very modest houses with deteriorating shutters and trim. Here—as across the state—the Warren campaign has coordinated its efforts with the state party and local officeholders so that doorknockers are talking not just about Warren but also about everyone else down-ticket. This integrates the newly recruited Warren volunteers with longtime salt-of-the-earth Democratic committee townsfolk. Their iPhone apps or printouts direct them to the homes of swing and sometime voters, telling them who lives there and how regularly each resident votes. Knocking on the door reveals more: whether a resident is lukewarm or enthusiastic, on which issues he or she needs more compare-and-contrast info about the candidates and whether the household would like a yard sign or a ride to the polls.

The Marlborough organizers told me that Warren volunteers have by now talked to nearly every one of the district’s swing and sometime voters that the party has uncovered on the rolls. While the Brown campaign and the state Republican Party would not return my calls or e-mails or speak to me when I dropped in, sources around the state said they’d seen no evidence of Republicans going door-to-door. The Massachusetts Democratic Party has the advantage in this kind of effort; it has forty-seven field offices and a deep organizing infrastructure that Walsh says he revived when he ran Deval Patrick’s campaign in 2006. The Massachusetts Republican Party has only ten field offices and no such grassroots history.

Warren’s second advantage is how well she’s done in three, very lively televised debates. She’s stayed calm and on point, talking effectively about policies and getting steadily warmer, more passionate and more personable about why she’s in the race. To win over the middle, Warren has named specific votes of Brown’s that play poorly in Massachusetts, tying him to the locally despised national Republican Party to undercut one of his two main selling points: that he’s an independent who votes what’s best for the state. Brown, meanwhile, has self-sabotaged his other selling point—his image as a really nice guy—by relentlessly attacking Warren on her native American ancestry. That may play well with his base, but undecideds find it frivolous and insulting, indicting his character, not hers. Brown’s “favorable” ratings have gone into free fall. Young independent or undecided women are much sought after by both campaigns, as they voted strongly against Coakley in 2010. Several women told me they were outraged by Brown’s condescension toward Warren and agree with her contention that it’s hard to trust a Republican Party that opposes—in 2012!—insurance for contraception.

The third factor on Warren’s side is the presidential election. Massachusetts is passionately in favor of re-electing President Obama. Romney is widely disliked here for his record as governor and for mocking the state on the campaign trail. Voters who might have stayed home in 2010 will turn out to vote for the president. In the January 2010 special election, the Brown/Coakley race was the only item on the ballot—and Brown’s supporters were the ones fired up enough to vote. This time, the enthusiasm is on the Democratic side.

Activists in swing districts around the state tell me that they are “pleased, very pleased” with what they’re finding as they canvass. The campaign has plenty of volunteers to remind those sometime voters to show up on November 6. By the time I left the Marlborough canvassing operation, the clouds had broken. Of course, anything can happen in the final week. But if the campaign keeps working as hard as it has been, the sky may be clearing for Warren.