WSJ’s Jennifer Levitz details the U.S. Senate race in Massachusetts that pits incumbent Republican Scott Brown against likely Democratic challenger Elizabeth Warren. AP Photo of Elizabeth Warren by Josh Reynolds.

LOWELL, Mass.—A battle here between Republican Sen. Scott Brown and likely Democratic challenger Elizabeth Warren in next year’s election is already drawing millions in out-of-state money because it could decide the Senate’s balance of power.

The race pits two nationally known candidates who have been elevated to prominence by separate populist waves. Mr. Brown, propelled by tea-party activists, scored an upset win in a special election in early 2010, capturing the seat long held by Democrat Edward Kennedy. Ms. Warren, a Harvard Law School professor and prominent consumer-finance watchdog, has tapped into the anti-Wall Street sentiment that is illustrated by the world-wide “Occupy” protests.

ReutersElizabeth Warren

Democrats hold a 53-47 Senate majority heading into the 2012 elections, but they are defending 23 seats, compared with only 10 for the GOP. So as a cushion against potential losses, Democrats hope to flip a couple of Republican-held Senate seats to blue—and they see Massachusetts, where Democrats outnumber Republicans three-to-one, as their best shot.

The race is “absolutely crucial” to Democrats, and because of the stakes, “it could be the bloodiest” Senate race next year,” said Jeffrey Berry, a Tufts University political-science professor.

A nonpartisan poll by the Center for Public Opinion at the University of Massachusetts at Lowell and the Boston Herald taken just days after Ms. Warren announced her candidacy in September showed 41% of registered voters favoring Mr. Brown, and 38% for Ms. Warren—which the university called a “dead heat,” given the poll’s margin of error.

Ms. Warren still faces a Democratic primary next September, but her most serious foes have already dropped out. In the quarter ended Sept. 30, she raised $3.15 million. Mr. Brown raised $1.55 million, boosting his campaign cash to $10.5 million.

Both Ms. Warren and Mr. Brown tell up-by-the-bootstrap life stories—he as the son of a single mother, and she as the daughter of an Oklahoma janitor in a family “pretty much hanging on by our fingernails.”

But they differ on how to fix the economy.

Mr. Brown “believes in comprehensive tax reform that lowers rates on everyone and makes the country more competitive economically,” said his campaign manager, Jim Barnett.

Ms. Warren says top earners and corporations should pay higher taxes, which she says would help the country avoid slashing programs such as school loans and services for the elderly. “America’s middle-class has been getting hammered for generations,” she said.

Supporters say Mr. Brown, known for his regular-guy persona, is a straight talker who is willing to defy rigid partisanship in Washington. “He’s not a cookie-cutter Republican” said Jeanne Kangas, interim chairwoman of the Massachusetts Republican Party.

Mr. Brown has broken with his party on several issues, including voting for the Dodd-Frank financial-services overhaul, and to repeal the ban on openly gay members of the military. “People like him are not many in Washington these days, and I think we need his voice,” Ms. Kangas said.

But some of his votes, including for Dodd-Frank, upset tea-party members who worked to get him elected, said Christen Varley, founder of the Greater Boston Tea Party. “I think there won’t be the same level of boots on the ground,” she said.

In response, Mr. Brown’s campaign manager said the senator promised voters he “would be an independent voice.”

Ms. Warren faces obstacles, too. After she said she provided the “intellectual foundation” for the Occupy Wall Street movement, the Massachusetts Republican Party tried to paint her as being too liberal for voters in the center, calling her in a video the “Matriarch of Mayhem.”

At a volunteer meeting in Brockton last week, she clarified—as she has done in other recent public events—that the movement is an independent one, but said, “I’ve been protesting what’s been going on at Wall Street for a very long time.”

Ms Warren’s fans, meanwhile, see her as an impassioned consumer advocate. On a recent day in Lowell, a working-class city north of Boston, Warren supporters filled an auditorium, pumping fists and promising to hold campaign signs. “Speak truth to power!” Bob Thornton, a retired janitor and independent voter told Ms. Warren.

Ms. Warren, an expert in bankruptcy law, moved into the public eye in 2008 when she led the congressional panel examining how bank bailout money was being spent.

“She was asking very simple questions, like, How does a bank get too big to fail? I thought, ‘My gosh, everything I have been thinking, I finally found a person who articulates it,’ ” said David Tolwinski, a Concord, Mass., independent voter and former high-tech executive.

She conceived the idea for the Consumer Financial Protection Bureau, a new part of Dodd-Frank that some conservatives have said will increase costs of doing business.

When Republicans vowed to block her Senate confirmation to head the consumer bureau, President Barack Obama picked Ohio Attorney Gen. Richard Cordray instead. That cleared the way for Ms. Warren to run for Mr. Brown’s seat.

Write to Jennifer Levitz at jennifer.levitz@wsj.com