For 20 years, Del. Joe T. May has represented the Virginia House’s 33rd District, a sprawling territory that runs from Leesburg to Winchester.

He has faced no opposition in his last two campaigns, but the incumbent is in a heated race this year with newcomer David LaRock, a Hamilton businessman who claims to be the more fiscally and socially conservative of the two Republicans.

With no Democrat on the ballot, Tuesday’s primary could determine the district’s next representative. Voters will cast ballots in House of Delegates races and for Democratic candidates for lieutenant governor and attorney general. The May-LaRock matchup is one of two competitive House contests in Northern Virginia.

LaRock, who became known locally last year as an outspoken critic of Metro’s planned extension of the Silver Line into Loudoun County, has said he can take on May despite the 10-term incumbent’s name recognition and fundraising advantage. May has raised about $150,000, according to campaign finance records, while LaRock’s campaign manager said the challenger had pulled in just over $55,000 as of May 29.

LaRock said he aims to win over conservative voters with a platform opposing tax increases, such as those in the landmark transportation funding bill the General Assembly passed this year. LaRock, who has said May is soft on gun rights and abortion, said he would oppose any additional firearms restrictions and would back legal rights and protections for the unborn from the time of conception.

Candidate guide to the 2013 Virginia primary election

“I’m a true pro-life conservative,” LaRock, 57, said in an interview. “That means 100 percent pro-life.”

May said he owns five guns and is staunchly opposed to abortion.

“I’m not opposed to guns, but I do think that there are common-sense rules to be applied to how you use them and how you carry them,” May, 75, said in an interview.

He added that he received a 100 percent rating last year from the Family Foundation, which opposes abortion. “I’d say they don’t probably give you 100 percent because you’re a screaming liberal,” he said. “But if you ask me if I vote for absolutely every law that comes before me, the answer would be no, because there is a certain amount of common sense to be applied.”

May has thrown some punches himself — including recent campaign mailers citing LaRock’s “arrest record,” referring to a July 2012 incident in which LaRock removed a sign from private property in Hamilton. LaRock said he thought the sign advertising an adult entertainment store was on public property and therefore displayed illegally. He was charged with a misdemeanor count of destruction of property.

LaRock was not taken into custody, but he signed a warrant of arrest acknowledging the charge and paid the resulting $81 fine, according to court records. LaRock said he provided a thorough explanation of the incident months ago and condemned May’s campaign literature as an attempt at “diversion and distraction.”

May stood by his campaign flier’s reference to the incident. “These are not spitting-on-the-sidewalk charges,” he said. “Virginia has great respect for private property.”

Separately, both candidates said the race should focus more on the state economy and transportation troubles in congested Northern Virginia.

May said his vote for the transportation bill shows his commitment to solving those problems. The $3.5 billion measure will fund transportation projects and repairs by raising sales tax rates and implementing a new wholesale tax on motor fuels. Revenue from particular areas — such as Hampton Roads and Northern Virginia — will be spent on projects in those jurisdictions, May said.

“I didn’t see that we have any choice but to address those projects and [maintenance needs],” he said. “I don’t want to be the legislator who voted ‘no’ for repairing bridges that might jeopardize the life and well-being of our constituents.”

LaRock counters that there should be a more financially efficient way to determine top-priority transportation projects. He also said that Northern Virginians will pay too much in taxes for projects that don’t benefit them. “There needs to be a ranking system for transportation issues, to focus on congestion relief and things like improving safety and reducing pollution,” he said. “Currently, I think it’s done rather arbitrarily, and a lot of money goes to pet projects around the state.”

Elizabeth Smith, a Purcellville retiree who recently hosted a neighborhood meet-and-greet for LaRock, said she was not impressed by May’s vote for transportation legislation.

“I like [LaRock’s] perspective that government is big and unwieldy and taxes are too high,” she said. “I never really thought of May as a conservative.”

During a round of door-to-door campaigning on a recent evening in Leesburg, May expressed confidence in his ability to connect with a broader range of voters.

Dan Wolfe, a registered Democrat and self-described moderate, spoke at length with May about the need for economic growth.

“We definitely need businesses working, we need jobs,” Wolfe said. He told the delegate that he would give him serious consideration, adding that he would prefer to support a moderate candidate rather than one who would encourage “political polarization” — implying May’s opponent.

But LaRock likes his chances in Tuesday’s primary.

“Before the big tax increase was passed by the legislature, you know, people told me this was impossible,” he said. “But having people react to that tax increase, and reacting to [May’s] voting record, I’m very optimistic. I think that this will turn to our benefit.”