Warren’s sole rival for the nomination, Marisa DeFranco, was unknown by 77 percent of voters in the poll, and it is uncertain whether she will attract the 15 percent support from state Democratic Party delegates to secure a spot on the Sept. 6 primary ballot.

Political insiders have been speculating fiercely over the level of damage the issue has caused Warren, who is considered one of the few capable of picking up a US Senate seat for her party in an otherwise difficult year for Democrats.

The controversy, which has dragged on for five weeks, has been the most difficult challenge for Warren, a first-time candidate who has at times given awkward and inconsistent answers on the subject.

The likely voters responded during a period of intense media coverage of questions over whether Warren used unverified claims of Native American ancestry to advance her academic career.

The poll of 651 likely voters was taken between May 25 and May 31 and has a margin of error of plus or minus 3.8 percentage points.

But, with the race virtually tied and demographics that favor Democratic candidates in Massachusetts, “this will be a really close race all the way through,’’ said Smith, director of the University of New Hampshire Survey Center.

“Overall, this shows the strengths that Brown has and it shows the problems, obviously, that the Warren campaign has had,’’ said Andrew E. Smith, the Globe’s pollster.

Still, the bottom line is that the race remains a toss-up, with Brown leading Warren 39 percent to 37 percent, largely unchanged from the Globe’s March poll that also showed Brown leading by two percentage points.

The poll shows Brown in a strong position. The incumbent’s job approval rating is at a comfortable 60 percent, with just 31 percent of voters saying they disapprove of the work he is doing in Washington.

The vast majority of voters (72 percent) said the issue would not affect their vote, but 31 percent of self-described independents - a critical voting bloc - said the issue makes them less likely to support Warren in November. The Harvard professor’s popularity has also risen one percentage point, to 48 percent, since the Globe polled in March, but the percentage of detractors has climbed more precipitously, by nine points to 32 percent.

But there are signs that the controversy has wounded the first-time candidate, whose entrance into the race came with a star power that galvanized Democrats and catapulted the contest into one of the most closely watched in the nation.

Despite a five-week drubbing over her claims to Native American heritage, Democratic Senate candidate Elizabeth Warren remains neck and neck with US Senator Scott Brown, a Republican, as she heads into Saturday’s state party convention, a new Globe poll shows.

The evidence of the impact of the Native American heritage issue on the campaign is similar to that in a Suffolk University poll released last week, showing the vast majority of voters did not feel it was a significant story.

Voters in the Globe poll seemed well aware of the issue, with 37 percent indicating they were very familiar and 33 percent saying they were somewhat familiar with it. But even among those who indicated they are paying at least some attention, 72 percent said it would not impact their vote in November.

“I wish it were about issues and we could understand the candidates more fully,’’ said Will Case, a 67-year-old retired marina manager from Orleans, and a poll respondent who said he typically votes Republican and probably will support Brown.

But that does not guarantee the controversy will end for Warren. Voters appeared divided over whether she has satisfactorily explained her assertion of Native American identity, with 42 percent saying she had not adequately explained it and 37 percent saying she had.

The potential impact, and limits, of the issue are evident in voters such as Jared Bettencourt, a 31-year-old union carpenter from Plymouth and a registered Democrat.

Bettencourt says he knows a little about the controversy, but is interested in learning more.

“It would be nice to know more about that because it kind of tells you what kind of person she really is,’’ said Bettencourt, who responded to the poll.

But either way, he is voting for Warren, he said, because of an overall dislike of Republicans.

The poll results among self-identified independents, whose votes Brown needs to win overwhelmingly in a state that traditionally favors Democrats, are particularly helpful to Brown. Fifty-seven percent of independents in the Globe survey said Warren had not fully explained the issue.

The Native American controversy has eclipsed the negative attention Brown has received from Warren supporters.

Only 19 percent of voters said they were very familiar with stories about Brown’s fund-raising from Wall Street interests, with 37 percent saying they were somewhat familiar.

And among those who were at least somewhat familiar, 66 percent said it would not affect their vote.

Brown also did well on a question that has, historically, often accurately forecast election winners. Voters, when asked who they think will win the race, regardless of their preference, chose Brown by a margin of 52 percent to 27 percent. Smith said that question is often a valuable predictor, especially farther away from an election, because it takes into account what poll respondents’ friends, relatives, and co-workers are saying about the candidates.

Laurie Petrie, a 60-year-old Chicopee Democrat who is unemployed, illustrates that point. She said she would be voting for Warren, but “I think a lot of people like Scott Brown; I wouldn’t be terribly upset if he beat her.’’

The poll reinforces Brown’s popularity, though both candidates remain well liked. When asked who is more likeble, 52 percent said Brown, while 26 percent said Warren.

Despite the apparent success Brown is having in projecting his message, he must still confront the difficulty of facing a well-financed and popular Democrat in a presidential year. President Obama, who will lead the Democratic ticket, remained ahead of Mitt Romney in the state, 46 percent to 34 percent, in the poll. The 12-point margin is smaller than the 16-point margin recorded in the March poll, but still strong.

Noah Bierman can be reached at nbierman@globe.com. Follow him on Twitter @noahbierman.

© Copyright 2012 Globe Newspaper Company.