In some ways, the Democrats are on a roll.

First, they beat expectations by easily winning the Virginia governorship earlier this month and nearly taking over the state legislature’s lower house. Now they have a shot at claiming a much more improbable prize: a US Senate seat in a special election Dec. 12 in deep-red Alabama, following allegations of sexual misconduct by Republican candidate Roy Moore.

But Democrats are hardly resting easy. The Clintons have roared back into the headlines, with some in the party now reevaluating former President Bill Clinton’s sexual escapades and Hillary Clinton’s controversial defense of her husband. Mrs. Clinton also caused a recent stir by questioning the legitimacy of President Trump’s election, handing critics an argument that she’s behaving just as she said Mr. Trump would if he had lost.

Elements of the larger context haven’t helped the Democrats: Their aging leaders have become fodder for Saturday Night Live parody. The Democratic National Committee is strapped for cash. And it’s locked in an internal battle between the “Bernie Sanders wing” and the “Hillary Clinton wing,” as it seeks to dig out of years of atrophy under President Obama – and an embarrassing book by former party chair Donna Brazile.

Then there are Trump and the Republicans, who are happily using Clinton for their own purposes. They have turned her into a sort of “bogeywoman” – beginning with the campaign chants of “lock her up” and continuing to this day with calls for a special counsel to look into her various alleged misdeeds.

In short, Clinton’s shadow still hovers over the party, part of the larger phenomenon of a party with many leaders – and therefore no leader. And as the Democrats regroup, they will need to answer an important question: Can they find a way to incorporate Clinton’s perceived positives – including as a role model for women looking to go far in politics – while avoiding her negatives?

“There are certainly people still adjusting to the fact that Barack Obama is no longer president, and to the stark difference that Donald Trump gives us,” says Jane Kleeb, chairwoman of the Nebraska Democratic Party. “I think a lot of this struggle to find our footing again is compounding all of that, because there is not one unified voice.”

The Democrats won’t have a true leader until they have a presidential nominee, and that’s two and a half years away. In the meantime, local party officials are getting used to the cacophony of voices that amount to a collective party leadership that is doing battle – and then at times cooperating – with Trump.

Ask Democrats who their leaders are, and the list is long: from Hillary Clinton, former President Barack Obama, and former Vice President Joe Biden; to Senator Sanders of Vermont (who isn’t even a Democrat, but an independent); to DNC chairman Tom Perez and vice chair Keith Ellison; to Sen. Chuck Schumer of New York and Rep. Nancy Pelosi of California, the minority leaders on Capitol Hill.

“On the one hand, such a long list is great, because it shows the kind of diversity and breadth of our Democratic Party,” says Ms. Kleeb, who was a progressive activist before becoming state party chair. “But on the other hand, it’s not great, because everybody knows that everybody’s fighting.”

Kleeb is a Sanders appointee to the DNC’s Unity Reform Commission, an effort to fix party processes and find common ground among the party’s factions. Last week, Sen. Tim Kaine (D) of Virginia called for the elimination of superdelegates, elected officials who can vote for whomever they want as the Democratic presidential nominee, without regard to the results of primaries and caucuses.

Senator Kaine’s status as an “establishment” Democrat – Clinton’s running mate in 2016, and a former DNC chair – gives his proposal added weight, as the Sanders wing seeks to make the party more “small-d” democratic. The Unity Reform Commission will meet next month and issue recommendations.

Other state party activists are more locally focused. Luis Heredia, a Democratic national committeeman from Arizona, sees opportunity for Democratic pickups in his state’s open US Senate seat, the governor’s race, and the House seat held by Rep. Martha McSally (R). But he agrees that the party’s message needs some work.

“Demographics cannot be destiny,” Mr. Heredia says. “We have a great opportunity with an emerging Latino electorate, with those energized young voters coming in. But in a midterm, you’ve got to give people a reason to vote. Democrats have to run against Trump, but also be bold, and carve out our message.”

In Wisconsin, where Gov. Scott Walker (R) is seeking a third term, state Democratic Party chair Martha Laning has eliminated the term “off year” from her vocabulary.

“We’re calling this the ‘build year,’ ” says Ms. Laning, who has boosted the staff from seven people to 19 since her election in 2015. “Right now, we’re in listening mode. We’re going out and asking people, what is the most important issue to them, and hearing them out.”

None of the state party officials interviewed expressed concern that Clinton could overshadow their efforts in next year’s elections – even in a red state like Nebraska.

“A lot of women and little girls saw Hillary Clinton as a transformative figure, just like many young people and African Americans saw Barack Obama as a transformative figure,” says Kleeb. “So no, we need her. I’m definitely not in the camp saying Nancy Pelosi and others who have been on the national stage need to move aside.”

Democratic pollster Mark Mellman doesn’t see anything unusual in Clinton’s ongoing visibility. “John Kerry went back to being a senator,” says Mr. Mellman, referring to the Democrats’ 2004 nominee. “He didn’t wither away to nothingness.”

He also doesn’t see Clinton trying to exert control over the party. “To my knowledge, she’s not involved herself in any of these internal debates about party processes … or even in policy debates,” he says.

A Democratic strategist, speaking not for attribution, sees the reigniting of debate over Bill Clinton’s presidency – particularly his sexual misbehavior – as a temporary phenomenon linked to the rash of allegations made against men in various spheres of public life, including Trump.

“Let’s be honest, whatever Bill Clinton did, he concluded what the public regards as a successful presidency,” says the strategist. Hillary Clinton’s continued defense of her husband – that he was held to account for his actions – may be uncomfortable for her now, but the moment will pass, he says.

Republicans can be expected to keep demonizing Clinton, as they seek to rev up their voters and avoid a wipeout in the 2018 midterm elections. Most recently, Republicans have been calling for a special prosecutor to look into the so-called Uranium One deal – and alleged links between hefty donations to the Clinton Foundation and the sale of shares of US uranium reserves to a Russian company, a deal approved by the State Department under then-Secretary of State Clinton, along with eight other agencies.

Clinton says the allegations have been “debunked” repeatedly, and that prosecuting her would make the country look like “some dictatorship.” For the GOP, keeping Clinton in the headlines serves an important political purpose.

“One way to keep a very fractured Republican Party together is just to bring up the name Hillary Clinton,” says Seth Masket, a political scientist at the University of Denver.

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For Democrats, bringing up Trump serves the same purpose. But even there, the party’s message isn’t uniform. TV ads by billionaire Tom Steyer calling for the impeachment of Trump are opposed by many Democrats.

“Impeachment at this stage, without a smoking gun, looks like a partisan ploy,” says progressive activist Robert Borosage. “It pleases the many liberals afflicted with doses of Trump derangement syndrome, but is seen as irresponsible at best by most everyone else.”