Democratic Party activists are conflicted over whether Hillary Clinton can take on Republican presidential front-runner Donald Trump in the general election, with some fearing she provides too much ammunition for the flamboyant businessman’s style of attack.

While Mr. Trump is leading the national polls and calling the shots in what’s become a circuslike GOP primary season, Mrs. Clinton tops a sedentary Democratic race with two other opponents respectfully nipping at her without doing much damage — and party stalwarts are happy to have it that way.

“I hear a lot of people saying, ‘You know, I’ve watched the Democratic debates and the Republican debates, and they’re so different. I’m sure glad I’m on the Democratic side and they’re talking about the issues. They don’t always agree with one another, but they explain why,’” said David Allen, a Democratic Party leader in Barnstead, New Hampshire. “Democrats have resolved themselves to not go into a circus and tear one another down.”

But Mr. Allen said he does worry about how the eventual Democratic nominee will stand up to the sort of withering barbs Mr. Trump has dished out to his own side.

“We’re going to start to have to look at how the [Democratic] candidates play against Donald Trump, because he’s certainly holding onto his lead in the Republican Party, and he has certainly played the Republican candidates in a way that has hurt some of his opposition, and I think people are going to start asking, ‘All right, who’s going to stand up under his type of campaigning?’” Mr. Allen said. “If Bernie [Sanders] is the candidate, Trump will play up how un-American socialism is, and if Hillary gets it, he will dig up everything in the past 40 years and use it — and won’t mince words in using it.”

Other activists say there’s a sense that, while it’s Mrs. Clinton’s turn to run, there’s no swell of on-the-ground enthusiasm for her to carry the party’s banner into the general election.

“I don’t think the [Democratic primary] race has generated all that much intensity,” said Ron Romine, chairman of the Spartanburg, South Carolina, Democrats, who is neutral in the race. “I don’t feel like anywhere in the state there’s all that much passion. The usual suspects will go out and vote, but there’s not an intensity that you might think there should be with the first woman.

“Hillary is so familiar, she’s been around forever. She has her supporters, and they’re going to go out and vote for her, so there’s not a whole lot to parse out,” he said. “You either like her or you’re not enthusiastic.”

Mr. Trump already has started taking aim at Mrs. Clinton, just as some activists had feared.

At a rally in South Carolina on Wednesday, the billionaire real estate mogul declared “war” on the Clintons as he explained why he wouldn’t attack Mrs. Clinton as “low-energy” — the term he used to devastate his GOP rival, former Florida Gov. Jeb Bush.

“I just don’t like to use the same thing twice on one of my enemies, because I consider them enemies,” Mr. Trump said. “We view this as war. Don’t we view this as war? It’s war, it’s war!”

Bothered by Mrs. Clinton’s accusation that he has a “penchant for sexism,” Mr. Trump continued to attack her husband, former President Bill Clinton, saying he was “one of the great abusers [of women] of the world.”

The Clinton camp this week said they would “stand up” to Mr. Trump. Deputy Communications Director Christina Reynolds said in a statement that “Hillary Clinton will stand up to him, as she has from the beginning,” citing Mr. Trump’s “demeaning” remarks about “women, immigrants, Asian-Americans, Muslims, the disabled or hard-working Americans,” adding that he has “pushed around nearly all of his fellow Republicans.”

Mrs. Clinton’s own supporters seem unfazed by the threat of Mr. Trump.

“I expected that to come up no matter who the [Republican] candidate was [and] the Bill Clinton past — I’m not the least bit surprised,” said Bonnie Chehames, who is campaigning for Mrs. Clinton in New Hampshire. “I can’t imagine Trump beating Hillary Clinton, and I don’t care what the polls say. The Republican Party will be fractured if Trump’s nominated, and that’s good for the Democrats.”

She also said Mr. Trump’s candidacy has helped Mrs. Clinton by taking press attention away from her during the primary season.

“The media isn’t really poking at her with negative comments. If Donald Trump were not the media superstar darling that he is, I’m sure that wouldn’t be the case,” Mrs. Chehames said.

Still, support for Mrs. Clinton as the Democrats’ champion in the general election remains lukewarm, especially among supporters of Mr. Sanders, her chief rival, who cite many of the same criticisms as Mr. Trump in arguing against her nomination.

“I just don’t trust her,” said Jason Frerichs, the Democratic Party leader in Montgomery County, Iowa. “I’m a progressive; that’s my value, and that’s what I want. I don’t need an ideological purity test, I just don’t trust her. She’s pivoted on too many issues important to me. I’m 38 [and] earn $45,000 a year. How can she understand what my life is like? She’s a millionaire. She’s a career politician. I just don’t see much excitement for her outside the baby boomers, who think it’s her time.”

Mr. Frerichs, who is caucusing for Mr. Sanders, said he understands Mr. Trump’s followers and believes Mrs. Clinton will struggle against him because she can’t match his charisma and doesn’t invoke any emotional connection or ties with her supporters.

“Bernie’s popular for the same reason why Donald Trump is popular: People are sick and tired of the same old politicians,” he said.

He said he would vote for Mrs. Clinton if she wins the Democratic nomination, but he refuses to campaign for her.

“I think we would see a low voter turnout with Democrats [in the general election]. She just doesn’t fire up the base,” Mr. Frerichs said. “Now, I could be wrong, and many women could come out just because she’s a woman, but most of the young women I see are caucusing for Bernie.”

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