Rep. Dave Brat became a political celebrity in 2014 when he ousted then-House Majority Leader Eric Cantor in a Republican primary, accusing him of having spent too much time in Washington and losing touch with his constituents.

Mr. Brat is now facing those same criticisms from Democrats, who said he hasn’t held a town-hall meeting in nearly a year and is ducking the concerns of Virginia voters in a state that’s increasingly tilting away from the conservative lawmaker.

Mr. Brat is poised to face the winner of the June 12 Democratic primary between Dan Ward, a Marine veteran who has the endorsement of VoteVets, and Abigail Spanberger, a former CIA operative who has the support of Emily’s List.

“Brat rode in to office on a very different wave — grass-roots conservative rebellion against the establishment,” said Mark J. Rozell, dean of the Schar School of Policy and Government of George Mason University in Virginia. “Now he’s a part of the GOP establishment trying to head off another potential anti-Trump mobilization.”

The Brat campaign said the Republican is taking the challenge seriously and “never stops traveling his district, listening to constituents.”

“They know Dave ran on a set of principles, and has kept his word. They see the positive impact of tax reform on our economy, and know it will help provide jobs for their kids,” the campaign said. “The Nancy Pelosi Democrats running in the 7th District want to repeal tax cuts, and even raise taxes by as much as $10 trillion.”

The National Republican Campaign Committee, the campaign arm of House Republicans, said Mr. Brat should easily surmount the challenge from what NRCC spokeswoman Maddie Anderson called a “motley crew of tier-three Democrats.”

She said the Democrats are pushing each other far to the left, putting them out of sync with a district Mr. Brat won by 15 percentage points in 2016.

Republicans say the race will offer voters a major contrast.

Mr. Brat backed last year’s $1.5 trillion tax cut and opposed last month’s $1.3 trillion omnibus spending bill, complaining that it would increase the national debt, did not include enough money for a border wall and allowed Planned Parenthood to still obtain taxpayer funding.

Both Mr. Ward and Mrs. Spanberger, meanwhile, have embraced Obamacare, called for universal background checks for gun purchases, and slammed the Trump tax cuts as a giveaway to the wealthy and fiscally irresponsible.

Democrats need to flip 23 seats to regain control of the U.S. House.

Rep. Barbara Comstock has long been viewed as the most endangered Republican in Virginia, but the target on Mr. Brat’s back has grown — particularly after Democrats’ huge wins in last year’s state elections.

New Gov. Ralph Northam led a sweep of the top three offices and Democrats flipped 16 seats in the House of Delegates, including a few that overlap the 7th Congressional District.

“The anti-Trump blue wave in Virginia last year changed all the political calculations and Brat’s race suddenly became competitive,” Mr. Rozell said. “He now has a real fight ahead of him.”

The Cook Political Report now lumps Mr. Brat in the second tier of vulnerable incumbents, rating his seat as “lean Republican.”

Another possible warning sign came in March when the Wason Center for Public Policy at Christopher Newport University released a poll that found Democrats were leading the generic ballot in Mr. Brat’s backyard by a 59 percent to 31 percent.

The shifting political landscape has emboldened Democrats, who believe the changing demographics of the district have made it more fertile ground.

“Dave Brat is vulnerable,” said Spencer White, Mr. Ward’s campaign manager. “There is this massive, almost unprecedented amount of energy from Democratic voters and Dave Brat has had to vote for all these bills that tie him to Donald Trump.”

Abbi Easter, chairman of the 7th Congressional District Democratic Committee, said she has worked in the political trenches for decades and has never seen voters so engaged.

“For those of us who have been here for 30 years, we are super happy to have reinforcements,” Ms. Easter said. “We have been out here fighting the fight and finally the cavalry has shown up.”

Mr. Ward had raised $550,000 and Mrs. Spanberger had pulled in $386,000, according to the most recent fundraising reports, which showed Mr. Brat has raked in $600,000.

Two years ago, Mr. Brat outraised his closest rival by more than $1 million.

House Majority Whip Steve Scalise, Louisiana Republican, is set to headline his annual “Breakfast with Brat” event next month in Richmond.

Republicans also say the math is on their side, pointing out that Mr. Northam lost the congressional district by about 4 percentage points in his 2017 governor’s race, in what was considered a great year for Democrats.

“The voters have a choice between the historic economic accomplishments — including a roaring economy and a historic tax cut — that have been made over the last year or to vote for Democrats who have done nothing but obstruct and put their heads in the sand,” said Garren Shipley, Virginia Communications Director at Republican National Committee.

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