The survey finds Warren leads Diehl 54 to 32 percent, with independent Shiva Ayyadurai polling at 6 percent.
Warren drew a lot of criticism recently for releasing results of a DNA test that confirmed she has some American Indian ancestry — a claim she has long made.
"I really have grown dissatisfied with her position on her Native American heritage," said James McCormack, a 57-year-old Army reservist in Plymouth who says he would pretty much vote for anyone who runs against Warren.
"There's no doubt in my mind that she used it to advance herself over others, and I find that unethical, and not somebody who I want a leader."
But McCormack is in the minority. Sixty percent of likely voters surveyed for WBUR say the Democratic senator's claim to Native American ancestry is not at all important in deciding which candidate to support in the Senate race.
There is a large gender gap.
"We have Elizabeth Warren with just over a 40-point lead among women," said Steve Koczela, president of MassInc Polling, who directed the survey for WBUR. "Male voters are actually roughly tied, so it's really women voters that are putting Elizabeth Warren over the top at this moment."
Diehl leads among unenrolled men and among men 50 and over. McCormack fits into both groups.
"The political tone is too hot," said McCormack. "There's too much rhetoric from both sides, and Liz Warren is flaming some of that. Geoff Diehl just seems a little bit more moderate to me on all of that, and somebody who, like Charlie Baker, currently, somebody who's more willing to compromise in order to get things done."
Sixty-nine percent of voters say they would be more likely to support a candidate who would make it a priority to work across party lines.
At the same time, 59 percent say they would be more likely to support a candidate who makes it a priority to stand up to President Trump.
"I could never send anybody to Washington who supports anything that [Trump] does," said Ellen Attridge, a stay-at-home mom in Essex. "Diehl is probably a decent guy. I think that once he gets into the maelstrom of the Republican stable in Washington, he won't be a good guy anymore."
The poll surveyed 502 likely voters in next Tuesday's election. Interviews were conducted last Thursday through Sunday. The margin of error is 4.4 percent.
"I like Elizabeth Warren," said Kate James, of Cambridge, who is among the 54 percent who say they'll vote for Warren. "I think she speaks up and stands up to things I want her to stand up to. I think she's a solid liberal, which I am."
But, some voters say they also want someone who offers new perspectives representing Massachusetts.
"We've had a lot of liberal Democrats as senators for years, and I would want somebody different, with a different philosophy, who comes at things with a fresh angle," said Philip Borrello, a pharmaceutical representative in Tyngsborough. "We've had Republican governors, and I think they've served us well, and I don't think it would be a bad thing to have an independent, different, fresh person in the Senate, at this point."
Borrello said that's reason enough for him to try Diehl.
Diehl leads among two more groups of voters: those with a high-school education or less, and residents of southeastern Massachusetts. He's from Whitman.
Diehl has focused, in his campaign, on Warren's presidential ambitions, saying she is not committed to Massachusetts. Sixty-three percent of voters surveyed say Warren should not run for president, but 64 percent say the fact that she may run for the White House makes no difference in their vote in this Senate election.
This segment aired on October 31, 2018.