Virginia Gov. Terry McAuliffe would appoint the Senate replacement for vice-presidential candidate Timothy M. Kaine if Hillary Clinton won the presidential election. (Katherine Frey/The Washington Post)

Hillary Clinton’s choice of Sen. Timothy M. Kaine for vice president has scrambled Virginia politics, leaving Gov. Terry McAuliffe with a tough decision: whom to appoint to the Senate if Democrats win the White House.

His choice would probably serve for about a year before running in a special election in 2017, and then have to turn around and compete for a full six-year term the following year.

The ideal appointee would be able to raise tens of millions of dollars in back-to-back years, excite the liberal base, inject diversity into a largely white, male 2017 ballot — and leave no state or congressional seats in Virginia vulnerable to Republican takeover.

Although Democrats hold all statewide offices — governor, lieutenant governor, attorney general and the two U.S. Senate seats — they acknowledge the bench is thin. The only obvious choice is McAuliffe himself, and he has said he is not interested.

The last time a governor did that in the late ’70s, voters were not pleased: Democrat Wendell Anderson of Minnesota, who died last week, was rejected by voters in his state.

Officially, McAuliffe is not ready to talk about whom he would appoint.

“It’s too early for us to be speculating on that,” his spokesman, Brian Coy, said Saturday. “The governor is focusing on doing his job and helping to turn Virginia blue for the Clinton-Kaine ticket.”

Most lists begin with the state’s three Democratic congressmen — Robert C. “Bobby” Scott, Gerald E. Connolly and Don Beyer.

As the first African-American elected to Congress from Virginia since Reconstruction, Scott has earned the right of first refusal, experts say.

“In terms of the ask, it would be a snub of the highest order not to go to him first,” said Bob Holsworth, a former political science professor at Virginia Commonwealth University. “Among the number of legitimate choices, Scott stands by himself as the first choice.”

Beyer, a former lieutenant governor and ambassador, and Connolly, the former chairman of the Fairfax County Board of Supervisors, have proved that they can raise money and win in vote-rich Northern Virginia.

All three publicly demurred, saying that delivering the state for Clinton this year is job No. 1.

“Governor McAuliffe will have many qualified individuals to choose from to fill Tim Kaine’s Senate seat,” Scott said in a statement. “I am confident the Governor will make a good choice.”

The gregarious governor also likes to say he thinks big, and his cabinet appointments reflect a philosophy of diversity. Those familiar with his calculus say he would relish the chance to make history by appointing Virginia’s first female or African American senator.

In that scenario, possible Senate picks include Del. Jennifer L. McClellan (D-Richmond), a corporate lawyer who has earned respect in the overwhelmingly Republican House of Delegates, and Molly Ward, who left a White House post to serve as McAuliffe’s secretary of natural resources.

Another potential choice, according to observers, is McAuliffe confidante Levar Stoney. The 35-year-old Virginia native is running in a competitive mayor’s race in Richmond this year and has political and fundraising chops. Stoney would have to overcome the perception that McAuliffe was gifting the seat to a friend.

The decision is ultimately up to McAuliffe, but observers say that Clinton and national Democrats will have input and that McAuliffe will weigh the results of polling and focus groups.

McAuliffe could also install a caretaker with no intention of running for re-election. That didn’t turn out well for New Jersey Gov. Chris Christie (R), who appointed his friend Jeffrey Chiesa to the Senate after the death of longtime senator Frank Lautenberg, a Democrat, in 2013.

The move angered his fellow Republicans and gave Sen. Cory Booker, then mayor of Newark, an easy path to election.

No matter what, McAuliffe can’t afford to make a mistake. Virginia’s Senate race will be the only one in the country in 2017, and it could determine the balance of power.

The race would also upend the usual fundraising dynamic in a gubernatorial election year and would probably draw huge amounts of money from the Democratic Senatorial Campaign Committee and the Democratic National Committee.

Campaigns would be able to join forces, for instance, combining federal contributions, — currently capped at $2,700 per donor — with cash from Virginia, which has no limits on political giving.

That cash is more critical than ever as Virginia increasingly reflects the close national divide between Republicans and Democrats. The once-deep red state is solidly purple and has seen many close races in recent years.

Kaine’s selection as vice president could also complicate Republican Party politics.

Last year, GOP strategist Ed Gillespie came close to unseating Sen. Mark Warner (D-Va.). He is riding that near-win to the 2017 governor’s race, where he will vie for the nomination against Rep. Rob Wittman (R-Va.), among others.

But after Kaine was announced Friday as Clinton’s pick for vice president, Hugh Hewitt, a conservative pundit and nationally syndicated radio talk show host, said a Gillespie do-over could draw more cash from the National Republican Senatorial Committee.

“Suddenly @RobWittman running for VA Gov seems much smarter as @EdWGillespie gears up for another Senate run, this time with NRSC support?” he tweeted.

Ed Gillespie quickly responded: “Actually Hugh, Kaine’s not gonna get elected VP .. and I am running for governor next year no matter what!”

Besides, many Republicans see the top choice for Senate as Ken Cuccinelli II, the polarizing former Virginia attorney general.

He made national news last week at the Republican National Convention for throwing his credentials on the floor in disgust after Donald Trump won the party nomination for president.

Cuccinelli’s name on the ballot could also motivate Democrats to vote, considering the outcry after Republicans discussed naming him a state Supreme Court justice during this year’s legislative session.

But if Cuccinelli bows out, Rep. Barbara Comstock (R-Va.) could parlay a successful re-election this year into a 2017 Senate bid, forcing Democrats to more seriously consider fielding a female candidate.

Further complicating the races, Republican Rep. Dave Brat, who ousted Eric Cantor, the former House majority leader, two years ago, said he would consider the job, too.