The Virginia governor's race offers a significant test of how much Trump's sagging job approval ratings could hurt Republicans in the 2018 midterm elections and gauges whether anti-Trump activism will benefit Democrats. Although the general election isn't until November, the poll suggests a hostile environment for Republicans.
Republican favorite Gillespie, who has a wide lead in the party's three-way primary race, trails both Democratic candidates by almost identical margins: Tom Perriello by 50 percent to 37 percent, and Ralph Northam by 49 percent to 38 percent among registered voters.
Voters seem to be punishing Gillespie for Trump's performance, which they don't like. Trump's job approval rating is at 36 percent, while 59 percent of Virginia residents disapprove of his performance as commander in chief. More than half say they "strongly disapprove," according to the poll, which was co-sponsored by The Post and George Mason University's Schar School of Policy and Government.
"Unfortunately for Republicans running this year, they will carry the negative taint of the Trump administration with them no matter how hard they try to separate themselves," said Mark Rozell, dean of the Schar School.
And there's no easy way out, because going too far in repudiating Trump risks alienating the party's base, which still approves of the president.
"It's a tough act to perform . . . I really don't envy them trying to do that," Rozell said. "The way it looks right now, that's a lose-lose situation for a Republican."
A majority — 77 percent — of Republicans in Virginia say they approve of the way Trump is handling his job, though just under half strongly approve, at 48 percent.
Among self-identified independents, more than 6 in 10 voters who disapprove of Trump support Northam and Perriello over Gillespie, with the Democrats receiving similarly wide support among independents who oppose the Republican health-care bill passed earlier this month by the House.
Fifty-eight percent of registered voters oppose the House Republican plan endorsed by Trump to replace the Affordable Care Act, also known as Obamacare. Just 34 percent of registered Virginia voters support the proposed replacement, the American Health Care Act.
Gillespie has been cautious on Trump — he was slow to endorse him last year and has been careful in responding to the regular flow of controversy that has marked Trump's presidency.
His problem is clear in the stance of a voter like Beverly Snead, 65, a political independent from Chesapeake. She voted for Hillary Clinton last fall but was willing to give Trump — and any Republicans running for governor — a chance this year.
But Trump's behavior in office has turned her off — and Gillespie's silence about it prevents her from supporting him, she said.
"I have no problem with Republicans, Democrats, running the United States. Just do the right thing," said Snead, who is concerned about Trump's possible ties to Russia and thinks he has hurt race relations with the "things that come out of his mouth."
"If you see someone in your party doing wrong, speak up and do the right thing," she said.
Gillespie is one of three candidates vying for the Republican nomination in the June 13 primary, along with state Sen. Frank Wagner (Virginia Beach) and Prince William County Supervisor Corey Stewart.
The winner will take on whoever prevails in the Democratic nominating battle, also culminating June 13, a tight contest between Northam, who is lieutenant governor, and former congressman Perriello. The poll did not measure general election preferences with Stewart or Wagner as the Republican nominee, both of whom trail Gillespie by a wide margin in the primary race.
Both Democrats are running hard against Trump, with Perriello leading that effort through an influx of national money, support from progressive darling Sen. Bernie Sanders (I-Vt.) and viral online videos.
Democrats' strength in the governor's race comes despite the lukewarm popularity of current Democratic Gov. Terry McAuliffe. At 49 percent approval and 25 percent disapproval, McAuliffe's ratings are largely positive but below the average for past governors and significantly lower than Maryland's Republican governor, Larry Hogan, who has a 65 percent approval mark in his state.
On the Republican side, the candidate who has most enthusiastically embraced Trump is Stewart, who was Trump's campaign manager last year in Virginia before being fired for protesting against party leaders he thought were not supportive enough of Trump. He has turned his verbal flamethrower on Gillespie for not strongly defending the president, but Stewart's stance hasn't translated into voter support.
Gillespie has double the voter support of either Stewart or Wagner among likely Republican primary voters, according to the Post-Schar poll.
Some Republican voters who approve of Trump say they would like a Republican governor to embrace him, but that it won't necessarily affect their vote in November. "It's important that he supports [Trump], but I think state government is quite a bit different than the federal government," said Nancy Hass, 52, a contract specialist from Virginia Beach.
Kevin Thompson, a 58-year-old Fairfax resident, said he wouldn't back an establishment Republican candidate like Gillespie in a primary but would still back him in a general election against a Democrat — "unless there's a very strong third-party candidate."
With overall Trump approval so low, though, the math is tough for any Republican nominee in the general election. Gillespie trails Northam and Perriello by similar margins even if you filter out people who are not all that interested in politics — those who did not vote last year, or in 2013, or who are not following the governor's race closely.
One factor that could help the Republican nominee is low turnout. Virginia elections typically draw far fewer voters in years when there is no presidential race. That can tend to favor Republican candidates, whose supporters generally are more likely to be white and older — groups that are statistically more likely to vote.
At this relatively early point in the race, similar shares of registered voters who are Democrats (59 percent) and Republicans (53 percent) say they are paying close attention to the election — though fewer than 1 in 5 of either party says they are following it "very closely."
Democrats are hoping that one side effect of the controversies around Trump is that more people are motivated to vote. Colin Dillon, 23, was old enough the last time Virginia picked a governor but was away at college and didn't bother.
Now a financial analyst living in McLean, he plans to show up this year for the Democratic primary as well as the general election. He credits Sanders for stirring his interest in politics, although his opposition to Trump is also driving him.
"I would say I'm definitely more engaged," said Dillon, who supports Perriello in the primary but would vote for Northam if he emerges as the Democratic nominee. "The current state [of Washington] has made me more focused on it and also more willing to bring up the discussion of 'you should vote' with people."
Monday is the last day to register to vote in the June 13 primaries.
The Post-Schar School poll was conducted by telephone May 9-14 among a random sample of 1,602 adults and 1,395 registered voters in Virginia, including landline and cellphone respondents, with a margin of sampling error of plus or minus three points among adults and registered voters.
Emily Guskin, Laura Vozzella and Fenit Nirappil contributed to this report.