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.