Despite giving her an overall approval rating of 57 percent, only 32 percent of Massachusetts residents said they would support Sen. Elizabeth Warren in a run for the U.S. presidency, according to a statewide poll of probable midterm voters released Wednesday.

The poll, conducted by the Suffolk University Political Research Center in partnership with The Boston Globe, surveyed 500 self-identified likely voters for the upcoming Massachusetts midterm elections on Nov. 6. Interviews were conducted by telephone, and topics ranged from local ballot questions to potential democratic nominees from Massachusetts for the 2020 presidential race.

David Paleologos, director of the Suffolk Political Research Center, said he thought the most surprising result of the survey was the discrepancy between Warren’s job approval and the percentage of residents who thought she should run for president.

“The questions about which prominent Democrat would you like to see run for president in 2020 kind of surprised me a bit,” Paleologos said. “I expected John Kerry, Deval Patrick and Elizabeth Warren to be the top three.”

Paleologos said the findings may be the result of some constituents’ desire to protect Warren from possible backlash. He said she may also face doubts among voters about whether a woman could defeat President Donald Trump.

“They [don’t] want to see her get attacked by Donald Trump everyday, or they [have] questions on whether or not a woman could get elected after a person as strong as and with an extensive resume as Hillary Clinton [did not] prevail,” Paleologos said. “They were worried almost to protect her.”

Maria Farias, 54, of Medford, said she would support Warren if she chose to run, but that she doesn’t think Warren could win.

“They both have criticisms against them, but I think he will win again,” Farias said. “They still can’t accept a woman to be president. They probably think a woman would be too soft.”

However, Paleologos said that he poll does not indicate that the people of Massachusetts do not support Warren, saying that that is “absolutely not the case.”

He explained that many of the percentages recorded in the results appear low because the survey is representative, including a mixture of Republicans, Democrats and independents who fall across the voting spectrum.

Warren earned a job approval rating of 86 percent among Democrats, but around only 42 percent of those same voters said they would support her running for president, Paleologos said.

“That is the biggest discrepancy in the polls,” Paleologos said. “There’s such a demand in Massachusetts for Donald Trump to be defeated, but people may see, after Hillary Clinton’s defeat, that it’s a risk not worth taking.”

Similar to what Paleologos said, Deepak Kulkarni, 62, said he would not support Warren running at this time because he thinks she is likely to lose.

“I like her, personally,” the Brookline resident said, “but because she is considered only slightly to the right of Bernie Sanders, I don’t think there is an appetite in the rest of the country for a politician that would present that particular face against Donald Trump.”

John Portz, a political science professor at Northeastern University, said it is not uncommon for voters to feel that elected officials should not end their terms early to run for another office, which is what would happen if Warren were to run for president.

“I don’t think that’s really unique to Massachusetts,” Portz said. “I think there is pushback when someone does that, and people feel that if you’re going to run for Senate, you should finish the Senate term.”

Another factor working against Warren if she ran for president, Portz said, would be the sense that many people want to see a candidate who is more neutral in the 2020 election.

“Bernie Sanders and Warren are on one end of the spectrum, and Trump’s on the other end,” Portz said. “I think there’s a pretty broad feeling that we need the center instead of one extreme or the other.”

Jason Adams, 36, of Fenway, said he would support Warren if he thought she could beat Trump.

“I personally don’t care for Elizabeth Warren, but I am inclined to vote for her against Trump,” Adams said. “I just don’t like her style. It doesn’t resonate with me … but to oust Trump, I’d vote for her.