Council member Jim Graham talks with Dana Miller, along with her young daughter, Kay Sank, at the Wilson Building on Thursday in Washington. (Katherine Frey/The Washington Post)

With more snow looming last weekend, Brianne Nadeau spent one last hour knocking on doors in LeDroit Park, hoping for a boost in a neighborhood that has chosen the same D.C. Council member since 1999, when she was studying political science at Boston College.

Speaking to a woman in her T Street NW doorway, Nadeau gave her spiel on the council’s Jim Graham: He is an out-of-touch incumbent whose ethical fumbles have become a distraction. The woman politely nodded and glanced at Nadeau’s campaign literature before agreeing to reconsider her choice for the April 1 Democratic primary.

Nadeau, a communications consultant, is hoping to rally enough residents to think twice about Graham, who for 15 years has enjoyed nearly iconic status in the fast-growing, highly diverse Ward 1 thanks to his quirky profile — thick-rimmed glasses and colorful bow ties — and close attention to constituent services.

A self-described ethical “lapse” has pitted Graham against a feisty, well-financed challenger in Nadeau, who hopes to capi­tal­ize on anti-corruption sentiment in the wake of last week’s guilty plea from a prominent businessman who financed an illegal, off-the-books effort to help elect Mayor Vincent C. Gray four years ago.

“There is a mood in D.C. right now,” Nadeau said Monday at her campaign office a few blocks north of the U Street corridor. “People are angry that their trust has been violated, and they should be angry.”

Graham acknowledged that Gray’s legal troubles haven’t done him any favors. And he conceded that Nadeau is one of the more serious challengers he has faced over the years. But he scoffed at her laserlike focus on his ethics record, calling it her campaign’s only plank. And he said he believes that his constituents still see him as someone who “gets things done.”

“There’s a lot of dissatisfaction right now, and some of that is certainly being passed on to me, but people are happy with my work,” Graham said Monday in a phone interview. “And that’s going to pay dividends.”

Both candidates tout their experiences as reflections of the ward’s vibrant makeup. Graham, the second openly gay elected official in District, rose to prominence in the lesbian, gay, bisexual and transgender community during more than 15 years at the helm of the Whitman-Walker Clinic. Nadeau is a former Advisory Neighborhood Commission member who helps promote progressive causes for nonprofit organizations in her day job at Rabinowitz Communications.

Nadeau has taken Graham to task for being only the second council member to earn the public disapproval of his colleagues. The nearly unanimous reprimand stemmed from a Metro investigation that found that Graham improperly mixed his roles on the council and on Metro’s board of directors when he expressed a preference for one developer over another for a property in his ward.

Graham denied he did anything wrong.

The reprimand left Graham looking more politically vulnerable than ever.

Before announcing that he would seek a fifth term, he formed an exploratory committee to weigh a reelection run — a relatively uncommon move for a veteran politician — and polled how the ethics issues would affect the race. Meanwhile, sensing a political heavyweight on the ropes, three candidates had already lined up to challenge Graham: Nadeau; Beverly Wheeler, a former council staffer; and Bryan Weaver, a former ANC commissioner.

In January, both Weaver and Wheeler dropped out of the race, with the former saying he would instead run as an independent in the general election. Wheeler cited her desire to spend more time with her family and threw her support behind Nadeau.

As the head-to-head race took shape, Nadeau picked up endorsements from council members Tommy Wells (Ward 6) and David Grosso (I-At Large), unusual moves given incumbents’ tendencies to endorse their colleagues or simply stay out of competitive races.

With Nadeau, “there’s no ethical cloud, where there is with Jim Graham,” said Grosso, who said he has recorded five or six robo-calls for Nadeau. “That makes a big difference.”

Nadeau is keeping up with Graham in the money race, raising $38,405 to his $43,490 for the five-week reporting period ending March 10, according to their campaigns’ latest filings. At the same time, the incumbent spent $39,172 and the challenger $66,658. Graham entered the final three weeks of the race with $62,903 cash on hand; Nadeau had $52,737.

Graham’s supporters say that his four terms are anything but a political liability. Kent Boese, an ANC commissioner who has endorsed Graham, said the incumbent has been “helpful in providing history and the back story of how we got where we are so . . . we know where we’re going,” especially as the Georgia Avenue corridor grows.

Buddy Moore, a community activist who has lived in the ward for 35 years, suggested that the Park View area could “slide back” under anyone else. Graham’s collaborative approach, Moore said, was key to transforming the neighborhood.

“If you invited Jim Graham to a meeting, he would do everything in his power to be there,” Moore said. “I don’t recall Jim Graham ever not showing up.”

With less than two weeks to the primary, both candidates say they are prepared for a close race, citing polls taken inside and outside their campaign over the past several months.

The race could come down to relatively new residents, such as Natasha Ghent-Rodriguez, who at a recent neighborhood association meeting asked Graham about young professionals apparently flocking to Nadeau. She said she supports the incumbent but posed the question because she wanted to know his response to what she sees as a real challenge for him: reassuring his constituents that he’s “still your man.”

“There’s only one Jim Graham,” she said during an interview Wednesday. “I don’t know if there’s enough to go around.”