Pollsters had major trouble spotting the surge of support for Corey Stewart in Virginia’s Republican governor’s primary this week, suggesting they still can’t figure out how to successfully survey Trump supporters.

Mr. Stewart, chairman of the Prince William Board of County Supervisors and onetime Trump campaign chairman in Virginia, ran as the Trump figure in the race, pursuing an anti-establishment message that centered around a tough approach to illegal immigration.

Polling — which was strikingly infrequent — showed Mr. Stewart failing to crack 20 percent support, trailing Ed Gillespie, the putative front-runner, by as much as 27 percent. In the end, Mr. Gillespie nipped Mr. Stewart by just 1 point, 44 percent to 43 percent. That left a lot of Trump-style Stewart supporters hidden in earlier polls.

Michael McKenna, a Virginia-based pollster and strategist, said the results should be another wake-up call.

“Researchers have to do a much better job of making sure that they are getting responses from all kinds of relevant populations,” Mr. McKenna told The Washington Times.

The sentiment swept through the polling community last year when surveys, while correctly catching Hillary Clinton’s popular vote lead, missed Donald Trump’s performance in a number of battleground states.

Media polls were particularly bad at finding Trump supporters. They undersold Mr. Trump’s support in battleground states he easily won, such as Iowa and Ohio, and outright whiffed on Wisconsin, Michigan and Pennsylvania by predicting a Clinton victory.

The poor showing sparked soul-searching, with pollsters debating their shortcomings.

Some speculated that Trump voters were shy about telling pollsters their leanings, while others said they botched the expected turnout. That meant pollsters were counting soft Clinton supporters who, in the end, didn’t show up.

Mr. Stewart said pollsters also don’t know how to properly measure how energized voters are online.

“There are a lot of people who were activated, who were awakened during the Trump campaign, and we still don’t know who is going to show up and vote in Republican primaries going forward,” he said as he surveyed the polls that undershot his support.

He said polls during most of the primary season were based on “bad samples” and tools such as social media are helping campaigns tap voters whom pollsters are missing.

“There was a very conventional way of determining the voting universe, which is old-fashioned and out of date,” Mr. Stewart said. “People are activated now more by social media, and they can be activated on a dime, whereas before it was predictable. You had the media and pretty much the same people showing up on the left and the right. Now, social media is transforming everything.”

One of the misses this year was a Washington Post/George Mason University survey in May that predicted a blowout. It showed Mr. Gillespie holding 38 percent support and Mr. Stewart well behind at 18 percent, barely ahead of Mr. Wagner’s 15 percent.

Mark Rozell, dean of the Schar School of Policy and Government, which teamed up with The Post on the poll, said a number of factors played into Mr. Stewart’s surprise showing.

“Low turnout, the ideological candidate with more intense support over-performs. This happens in low turnout, off-cycle campaigns,” Mr. Rozell said.

He said the primary vote suggests Mr. Gillespie will have a tough time in the general election.

One poll got the Republican race almost exactly right. Change Research’s June 8-10 poll showed Mr. Stewart with a 42-41 lead over Mr. Gillespie, with Mr. Stewart’s supporters more committed to showing up.

But Change Research’s success was coupled with a total botch in the Democratic primary, where the organization had former Rep. Tom Perriello easily winning. Instead Lt. Gov. Ralph Northam triumphed handily.

Pat Reilly, a spokeswoman for the firm, said they build their survey pool online, chiefly from Facebook. That allowed them to gather a much broader sample size than any of the traditional phone line surveys, which have a huge no-response rate.

“Stewart’s core support was among Donald Trump’s biggest fans — those who rated Trump a 9 or 10 out of 10 — where he led over Gillespie by nearly 20 points. Because we were polling right up until the closing days of the election, we were seeing that sentiment online,” the spokeswoman said.

Larry Sabato, a political scientist at the University of Virginia, said the primary polls in Virginia this year “were generally awful.”

“The polls generally created two themes that hardened into conventional wisdom. First, Gillespie was the runaway favorite and the GOP primary wasn’t much of a race. Second, Northam and Perriello were in a death struggle in a very close primary that Perriello was on the verge of winning. Both propositions were absolutely wrong,” he said.

The dangers of missing polling targets are myriad, but overlooking Trump voters could skew perceptions of the president’s job approval and popularity or, in this case, the unpopularity of House Republicans’ health care bill.

“Researchers need to be honest with themselves. They are viewed by some significant chunk of people — and usually the same kind of people — as part of the problem,” Mr. McKenna said. “That may or may not be deserved, but it is the reality. That affects response rates, drops, and all kinds of problems in survey research in politics.”

David Paleologos, who runs the Suffolk University Poll, which didn’t survey in Virginia, said missing voters is a problem but not a major one.

He said state primaries, such as the Gillespie-Stewart-Wagner race, do pose pitfalls, with a large number of undecided voters and more than a binary choice between two candidates. A lot of Stewart voters could have been hiding in other categories.

“If you have a higher undecided and you have a candidate like Trump or a supporter of Trump‘s, it’s easy to mask your support in the undecided column,” he said.

Mr. Paleologos, though, said that is probably not as big an issue for looking at Mr. Trump’s job approval ratings, where the question is straightforward and there aren’t a lot of ways to respond.

“When you have a binary question where it’s approve or disapprove and the sample frame is correct and all the other boxes are checked on the design, pollsters are pretty close to the outcome,” he said.

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