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Senators Elizabeth Warren and Bernie Sanders of Vermont are locked in a statistical tie ahead of the Massachusetts primary on Tuesday, according to a poll released Saturday by Suffolk University, The Boston Globe, and WBZ-TV, raising the possibility of an embarrassing loss for Warren on her home turf as her presidential campaign struggles to find a single contest she can win.

The poll found 24 percent of respondents leaning toward or planning to vote for Sanders, the current front-runner for the Democratic presidential nomination, and 22 percent for Warren, with the difference within the poll’s margin of error of 4.4 percentage points.

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The poll comes as Sanders mounts an all-out offensive to win Massachusetts, one of 14 states holding primaries on Super Tuesday, that included rallies in Springfield and Boston in the last two days, which some Warren allies viewed as a brazen attempt to humiliate her. Warren’s campaign sent cascades of volunteers to canvass the state and held 80 organizing events. But her supporters sought to tamp down expectations and suggested she did not need a victory in her state to remain in contention.

“It comes down to not who is winning how many states, but how many delegates you are getting in each state,” said Boston City Councilor Michelle Wu, who has endorsed Warren. “There’s not a must-win state for anyone.”

Prior to the South Carolina primary Saturday, Sanders had 45 delegates and Warren had 8.

The Suffolk/Globe poll of 500 likely voters in the Massachusetts Democratic primary found another tight skirmish for third place, with former New York City mayor Michael Bloomberg at 13 percent, former South Bend, Ind., mayor Pete Buttigieg at 12 percent, and former vice president Joe Biden at 11 percent, all within the margin of error. The poll was conducted Wednesday through Saturday with live callers surveying respondents on landlines and cellphones.

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If the rallies Sanders held in Massachusetts this weekend are any indication, he appears to be drawing significant support from voters Warren ordinarily could count on.

“We in Massachusetts kind of owe her our vote — you know, favorite daughter,” said Jon Weissman, 73, a retired letter carrier from Granby who went to Sanders’ rally in Springfield on Friday. He said it wasn’t until Warren “waffled on single-payer” health care that he decided to vote for Sanders instead.

As Sanders campaigned on her turf, Warren spent Saturday hopping among South Carolina, Arkansas, and Texas.

“This is winning,” she told reporters in Columbia, S.C., as she touted voter enthusiasm for her ideas such as a wealth tax. She did not directly answer a reporter’s question about whether she needed to win Massachusetts.

“It’s always been about getting out and talking to as many people across Massachusetts, but across the country as I can, and that’s what I will keep on doing,” Warren said.

Also, the poll found voters roughly split whether, in their gut, they believe President Trump will be elected. Two-thirds of respondents said they preferred a unifier as the nominee, compared to 19 percent who wanted a fighter (Warren has campaigned as both). A majority, 54 percent, said they would be comfortable with a billionaire as the nominee. And there was broad backing in the poll for Medicare for All, the universal health care proposal supported by Sanders and Warren, with six in 10 respondents favoring it.

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The main drama is in the ground war between the Warren and Sanders campaigns in Massachusetts. That played out in real time on Friday as Sanders’ campaign launched a four-day “Berniepalooza” festival of music and canvassing, with Sanders himself appearing before 4,750 people in Springfield Friday night. On Saturday, the Sanders campaign said at least 13,000 supporters attended a rally on Boston Common, where chants of his first name seemed to bounce off the State House’s glinting golden dome.

In Boston, Sanders did not mention Warren by name, although he seemed to take a dig at the Persist super PAC that has spent $14 million on ads on Warren’s behalf — an effort she has not disavowed despite her long-held opposition to dark money in politics.

“We don’t have a super PAC, we don’t want a super PAC, we don’t need a super PAC,” Sanders said, as the crowd roared. (Sanders does, however, have the support of groups such as Our Revolution, which does not have to disclose its donors, and the super PAC National Nurses United.)

Warren herself has not headlined a campaign event in Massachusetts since a speech in Boston Dec. 31. Her campaign is currently aiming to amass as many delegates as possible on Super Tuesday to remain in contention, after finishing third in Iowa and fourth in New Hampshire and Nevada. Some polls suggest she could exceed the 15 percent threshold necessary to be awarded delegates in California, Texas, and Colorado.

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Her supporters back home held get-out-the-vote events around the state on Saturday and touted 176 endorsements from Massachusetts officials, including Congressman Richie Neal, who announced his support for her just on Friday. Nonetheless, they have been forced to acknowledge Sanders’ popularity here in recent days.

“Bernie did very well here in 2016 and we’re sure he’ll continue to do well because that’s evidence of the shift in the electorate and a mandate for a more progressive country,” said Representative Ayanna Pressley in an interview on Friday. She added: “We’re just head-down, focused on the work.”

On Saturday morning, with an ad for Warren by the Persist PAC ad airing on the television behind him, Mike Likova, 65, a bartender at City Table on Boylston Street who supports the Massachusetts senator, shrugged off the show of support for Sanders going on just a mile away.

“He’s entering the wrong territory,” Likova said.

But the Suffolk/Globe polling data suggest Massachusetts could be Sanders territory after all.

“We have a close race,” said Suffolk University pollster David Paleologos.

Sanders is beating Warren 35 percent to 23 percent among nonwhite voters, and has a 23-point margin on her among voters under the age of 35.

“He’s sort of spearheaded the movement in the Democratic Party toward free health care, socialized medicine,” said Jason Monsignore of Medford, a security company employee in his late 20s who supports Sanders. “He’s the one who’s going to try to do what he’s going to say.”

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Sanders also leads Warren among male voters, while Warren edges him among women voters. While she tops Sanders among voters over the age of 65, other candidates are also not far behind in that cohort, with Biden at 19 percent, Buttigieg at 15 percent, and Bloomberg at 16 percent.

Warren and Sanders each get the support of 32 percent of liberal voters, Paleologos said, but he performs significantly better with moderate voters. The polling data suggests Bloomberg has cut into his advantage with independent voters.

“The categories Sanders is winning, he’s winning outright and by large margins,” Paleologos added.“In categories where [Warren] needs to grow, there are other viable candidates holding her down." He added, "Although she’s close, it’s like, ‘Where do you make it up?’”

Joan Peterson McWilliam, 79, said she was voting for Warren because she wants her to hold the state, even though she does not think the Massachusetts senator will ultimately win the primary.

“If we were inclined to elect women, I think she would be terrific," McWilliam said. “She stands up to special interests, to banks, to corporations — she’s not afraid.”

Linda Benoit, a 62-year-old social worker, said she had voted early for Sanders because she saw him as the candidate with “momentum.”

Sanders’ Friday night rally even drew one of Warren’s endorsers, Springfield City Councilor Adam Gomez, who watched from the crowd, although he insisted he was sticking with Warren when approached by The Boston Globe.

“You see that Western Massachusetts is fired up for Bernie, it never stopped,” he said. Referring to Warren, he said: “I don’t think she necessarily needs to win, but she needs to do well.”


Jess Bidgood can be reached at Jess.Bidgood@globe.com. Follow her on Twitter @jessbidgood.