Brown has continually criticized Warren for listing herself as Native American in a legal directory and in some official documents at universities where she has been employed. She has said her belief in her ancestry, though undocumented, is the result of family lore. She has said the listing did not benefit her career, and numerous people involved in her hiring have backed that up. But she has been unwilling to ­release personnel records, as Brown has demanded.

The poll suggests most voters are now familiar with the controversy, with 79 percent in the survey saying they were at least somewhat familiar with it, compared with 70 percent who said so in May.

Of those who knew of the controversy, 71 percent said it would have no impact on their vote, while 24 percent said it would make them less likely to support Warren. Notably, 10 percent of Obama’s supporters are among the group who said the controversy makes them less likely to vote for Warren.

John Cunningham, a 43-year-old Democrat from ­Bellingham who participated in the poll, is one of those voters. “It was just saying to me that, eh, I don’t know if I can really trust this person,” Cunningham said. He said he plans to vote for Obama and for Brown.

Brown has broadened his ­attacks the last several weeks to include criticism of Warren’s legal work on behalf of two major corporations, Travelers Insurance and LTV Steel, in an attempt to undermine her reputation as a consumer advocate. The poll did not directly ask about those issues, but Smith believes Brown has no choice, from a tactical standpoint, but to go negative, given his need to neutralize Warren’s built-in advantage in party support.

The poll shows no significant backlash so far against Brown for attacking Warren, Smith said, pointing out that when respondents were asked to select the more likable candidate, 58 percent said Brown, compared with 27 percent who chose Warren.

But Warren remains popular for a political newcomer. In a separate question, 53 percent of voters said they view her favorably, compared with 36 percent who view her unfavorably, a ­ratio that is largely unchanged since May. Warren leads Brown among women by 12 percentage points, a larger margin than the 3-point advantage Brown has with men.