By NEIL KING JR.

The Virginia governor’s race long has been considered one of the country’s marquee political contests of 2013, pitting a national tea-party hero, Republican Attorney General Ken Cuccinelli, against a close friend of the Clintons, former Democratic Party chairman Terry McAuliffe.

But the plot has thickened amid a spat among the state’s Republicans over the party’s tone and direction. Some conservatives fear the fight could wound the GOP as it seeks to broaden its reach among independent voters in a state where Democrats have made big gains.

Associated PressAttorney General Ken Cuccinelli, left, is a Republican running for governor of Virginia.

The governor’s race will be closely watched, in part because there are few other contests nationally in an odd-numbered year, but also because it follows the Republican party’s loss in last year’s presidential election.

The Virginia matchup looked relatively settled just weeks ago, after Mr. Cuccinelli managed to outmaneuver the man long seen as the Republican heir apparent, Lt. Gov. Bill Bolling.

The Register & Bee / Associated PressLt. Gov. Bill Bolling, the long-seen Republican heir apparent for governor of Virginia.

But after dropping out of the nomination hunt late last year, Mr. Bolling now is crisscrossing the state to drum up support for a possible independent run, all the while casting aspersions on Mr. Cuccinelli and what he sees as the party’s shrinking appeal to independent and moderate voters. Mr. Bolling quit the race after concluding the odds were stacked against him in the coming state nominating convention.

“Instead of becoming a big- tent party, we are rapidly becoming a pup-tent party,” Mr. Bolling said in an interview Friday. A lifelong Republican who spent a decade in the state Senate and is in his second term as lieutenant governor, Mr. Bolling said he was “very concerned about the leadership and direction of the Republican Party in Virginia.”

Associated PressFormer Democratic Party chairman and Clinton family friend Terry McAuliffe.

He plans to meet Monday with around 50 business leaders in Northern Virginia, including dozens of Mitt Romney’s biggest backers in the state last year in his presidential run. Some who plan to attend said they worry that Mr. Cuccinelli would steer the party in the wrong direction.

“Virginia will be this year’s big indicator of where the Republican Party is going and whether we can appeal to independents and win elections,” said one of the state’s top GOP fundraisers, Bobbie Kilberg, who is hosting Monday’s event and supports Mr. Bolling. “Ken Cuccinelli has put a very strong focus on social and culture issues, which is not where we want to be.”

Cuccinelli adviser Chris LaCivita rejected suggestions his candidate plans to run on social issues. “We are going to keep our focus on jobs and the proper role of government,” he said.

Since being elected attorney general in 2009, Mr. Cuccinelli gained notice by challenging the legality of President Barack Obama’s health-care overhaul and attacking the Environmental Protection Agency’s right to regulate greenhouse gases.

The former state senator and father of seven has backed crackdowns on illegal immigrants and pushed to allow college students to carry guns on campus. He supported a controversial bill in the Virginia legislature last year that requires women seeking an abortion to get an ultrasound first.

Mr. Bolling said his own record doesn’t differ markedly from Mr. Cuccinelli’s on issues including opposition to gay marriage and abortion. “We’re both very conservative guys,” he said.

But he and his supporters argue that Mr. Cuccinelli’s confrontational style threatens to alienate less partisan voters.

Republican Gov. Bob McDonnell, a longtime Bolling ally who promised to support his campaign for governor, has nonetheless thrown his weight behind Mr. Cuccinelli, hoping to tamp down an intraparty feud. Virginia law bars governors from seeking re-election.

The discussion comes as Virginia, once a firm supporter of the GOP in presidential races, backed Mr. Obama twice. Democrats also won the last three races for U.S. Senate.

The current fight has its roots in Mr. Cuccinelli’s success last year in taking over the party’s central committee, which then switched the nominating contest to a party convention dominated by conservative activists, set for May, instead of an open primary.

Recent polling found the two Republicans fairly evenly matched, while Mr. McAuliffe edged both men. The most recent financial disclosures, in June, had Mr. Bolling with $1.5 million in cash on hand, compared with $627,000 for Mr. Cuccinelli.

Some party leaders worry the fight could jeopardize Mr. McDonnell’s policy aims as he eyes a 2016 presidential run, if Mr. Bolling decides to use the coming legislative session to cut a more moderate path.

Mr. Bolling has the power to break ties in the evenly divided state Senate, so he could be the decisive vote on issues ranging from highway construction to gun control to the question facing the state of whether to legalize uranium mining. Business interests, promising a boom in jobs, are pushing to lift a current ban on uranium mining in a state rich in the material. Mr. Bolling has come out against lifting the state’s uranium-mining ban, an issue McDonnell aides say the governor is still weighing. Mr. Bolling also said he opposes the governor’s suggestion last month that the state consider arming teachers to protect students in classrooms, a proposal floated by the National Rifle Association.

Republicans worry the clash will make matters easier for Mr. McAuliffe, the all-but-certain Democratic nominee, who is sure to have campaign help from former President Bill Clinton.

“The big question is whether this going to be a Republican team effort or a factional effort,” said Tom Davis, a former Republican congressman from northern Virginia. “The party is going to need all wings flapping to pull this off, and right now we’re not where we need to be.”

Write to Neil King Jr. at neil.king@wsj.com