By Noah Bierman Globe Staff

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.

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.

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.

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.

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.

‘‘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.

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.