Elizabeth Warren spoke to a group of newspaper publishers in Boston last week, giving an important speech to people with the power to influence media coverage of her Senate race against Republican Scott Brown.

The Massachusetts Newspaper Publishers Association held its annual meeting at the hallowed Anthony’s Pier Four, giving the candidate a stunning backdrop for her speech: the Boston waterfront, bathed in sunshine on the first day of December. As the captains of media finished up their choice of scrod or chicken, Warren told a story most of her audience already knew if only from her recent television commercials—the story of a girl who, thanks to the vagaries of middleclass economic insecurity, might never have reached her full potential were it not for a government student loan program.

The fact that Warren ended up being “a fancy-pants professor at Harvard Law School,” she said, is testament to post-Depression government policies that ushered in “a half-century of economic peace” following two hundred years of economic turmoil—policies that have been steadily eroded, she said, since about 1980.

It was easy to hear the teacher in Warren as she laid out the history of market volatility tamed largely by three 1930s-era policies: the establishment of the Federal Deposit Insurance Corp. (FDIC) to make banks safe for depositors; passage of the Glass-Steagall Act “to make banks boring,” Warren said, by limiting speculation and preventing conflict of interest; and “putting a cop on the beat” in the form of Wall Street regulators.

Of course, Warren’s history lesson resonates today due to the 2008 financial crisis and the government bailout of some of Wall Street’s biggest banks. Her campaign, she told the publishers, represents her commitment to continue the work she’s done in the last two years, serving as chair of the congressional panel overseeing the bailouts and helping to create the Consumer Financial Protection Bureau against fierce opposition from Wall Street lobbyists. Warren’s candidacy turns largely on her identity as someone with the guts and brains to fight Wall Street on behalf of the middle class—a fight, she said, that America can’t afford to lose.

As political performances go, Warren’s 20-minute luncheon speech, followed by questions from the audience, was strong; she was energetic, entertaining, smart, funny. Stump speeches like this one, as well as her recent TV ads, are clearly working: as Warren left the banquet room, one of the reporters in the scrum that gathered around her told the Democrat that she’s just nudged ahead of Brown in the polls.

But while it was hard to imagine Warren’s being in a significantly better position at this stage, it was also easy to see some potential trouble ahead.

The most obvious trouble: Warren is running for the nomination of a political party that, when it comes to playing nice with Wall Street, is nearly as bad as the Republican Party. When she noted the other day that her opponent “has been identified by Forbes magazine as one of Wall Street’s favorite senators,” Warren failed to acknowledge that two leading Democrats, Senate Majority Leader Harry Reid and Sen. Chuck Schumer (D-New York), ranked well above Brown on the Forbes list. The oversight was promptly pointed out in the next day’s Boston Herald.

During the question and answer portion of her presentation last week, I asked Warren why she is comfortable in the Democratic Party. With a laugh that showed she understood the thrust of my question, Warren explained that she’s far from being a partisan: “I’ve belonged to different political parties … and to no political party at all.” She said she chooses to be a Democrat now because Democrats are willing to talk about the issues dear to her: “What’s really driven me for all my life is this question about the economic survival of America’s middle. Without that, we don’t survive economically … politically … socially and spiritually.”

As her answer reveals, Warren can look like a one-issue candidate. This is both a strength, given the importance of the issue and the attention she’s earned for her battles with Wall Street, and a weakness: some voters, as well as her Democratic Party advisors, may prefer a more traditional-looking candidate who can speak convincingly about a wide array of parochial issues. To the degree that she moves from her central issue, where she has great passion and a lot to say, she risks appearing homogenized, pre-packaged.

Warren confronts a similar challenge as she faces growing criticisms of her recent comment about being the “intellectual mother of Occupy Wall Street.” While the protesters embody the middleclass anxieties and antipathies that are at the intellectual and emotional center of her campaign, attack dogs like MassGOP’s Tim Buckley clearly hope the protests will wear thin with the public and become an albatross for Warren.