Voters in Virginia’s 33rd Senate District will cast ballots Tuesday in a special election to fill the seat vacated by Attorney General Mark R. Herring — a contentious three-way race that could determine control of the state’s evenly divided Senate.

The trio of candidates vying for the seat — Democrat Jennifer Wexton, 10th Congressional District Republican Committee Chairman John Whitbeck and former state delegate Joe T. May, a veteran Republican who is running as an independent — have had only a few weeks to organize their campaigns and rally supporters across the district, a politically competitive territory spanning parts of Loudoun and Fairfax counties.

But that didn’t stop the election, with control of the General Assembly’s upper chamber hanging in the balance, from unfolding as a high-stakes, high-dollar and high-drama contest.

Polls opened at 7 a.m. in Loudoun and Fairfax counties, despite predictions of a major snowstorm that shuttered schools and the federal government. Elections officials recommended that residents vote early to avoid slippery roads.

With the Virginia Senate divided in a partisan 20-20 split, the two seats left open by Herring and Lt. Gov. Ralph S. Northam create an opportunity for Republicans, who control the House of Delegates by a wide margin, to secure a 21st, tie-breaking vote. If Democrats retain both seats, Northam would act as a tie-breaking vote, limiting the GOP’s political leverage against Gov. Terry McAuliffe (D).

The off-cycle election was already expected to produce low turnout.

Republicans typically do a better job of motivating their grass-roots supporters to come to the polls in such contests, and both sides were watching anxiously to see if the storm gave the GOP further advantage by suppressing voter turnout even more.

The outcome of the special election to fill Northam’s seat in the 6th Senate District remains uncertain. Democratic Del. Lynwood W. Lewis was certified the winner by just nine votes, prompting Republican Wayne Coleman on Thursday to request a recount.

J. Garren Shipley, spokesman for the Republican Party of Virginia, said the narrow margin demonstrates the impact of the GOP’s campaign strategy.

“Pundits wrote that race off as a Democratic lock,” he said. Virginia Republicans, he added, were similarly concentrating their efforts on the ground to secure a win for Whitbeck in the 33rd District.

“This has been a very short election cycle, but we know it’s a critical seat,” Shipley said.

Campaign finance records as of last week showed that Democrats are putting up a powerful fight of their own: Wexton’s campaign has raised more than $645,000 in contributions — vastly outspending Whitbeck, who reported about $235,000 in donations, and May, who has raised $168,000, according to the nonpartisan Virginia Public Access Project.

Michael Sargeant, executive director of the Democratic Legislative Campaign Committee, said Democrats had focused a “strong concerted effort” on rallying support and raising funds for Wexton.

“There’s a really strong grass-roots field operation working every day with her,” he said. “We’re taking this election very seriously.”

Wexton has used her substantial campaign coffers to launch an advertising blitz, including a television ad that drew sharp criticism from Republicans. In the ad, Wexton cites her experience trying rapes cases as former Loudoun County prosecutor.

“In the Virginia Senate, I’ll fight just as hard against tea party Republicans who would take away a woman’s health care and her right to choose, even in cases of rape and incest,” she says in the video.

The Republican Party of Virginia quickly condemned the ad, claiming that Wexton was comparing her political opponents to rapists. Pat Mullins, chairman of the Republican Party of Virginia, said in a prepared statement that the ad proved Wexton was unfit for office.

“Jennifer Wexton is running to represent all of the people in the 33rd Senate District, not just liberal Democrats like her,” Mullins said. “If Jennifer Wexton is truly writing off people who disagree with her as no better than rapists, then she has no business in politics at all.”

Wexton’s campaign said that claim was “ridiculous” and a false comparison.

“The ad is about Jennifer’s record as a fighter and a defender of women, and it’s comparing her fighting to defend women in court . . . to fighting to protect them in Richmond,” said Wexton campaign spokesman Mitchell Norton.

Whitbeck jumped at the chance to target Wexton’s experience as a prosecutor. His campaign released a statement detailing four of Wexton’s cases in which charges against an accused rapist were dropped or reduced, resulting in lesser sentences.

Wexton said she stood by her record as a prosecutor.

“When you prosecute thousands of cases, it’s inevitable that there are going to be some that turn out in a way you don’t want them to, for many, many reasons,” she said.

Whitbeck has also taken aim at May, claiming that the veteran legislator is not conservative enough and equating his position to Wexton’s.

“Jennifer Wexton and Joe May — two liberal politicians, the same risky agenda that hurts our economy,” Whitbeck’s TV ad declares.

May, a longtime Republican lawmaker who cut his ties with the GOP last year, has generally remained above the fray and positioned himself as the moderate choice of the three.

May’s campaign ads have maintained an upbeat tone and focused on his career as an engineer — including his “cool, but kind of nerdy” invention of the yellow first-down line that appears during televised football games — and his decades of experience in public office.

Despite his official break from the GOP, May has said he would caucus with Republicans if elected — giving the party an added chance at securing a voting majority in the Senate.