Rally With Trump? Some G.O.P. Candidates Aren’t Thrilled About It.

Former President Donald J. Trump is preparing to swoop into Ohio on Saturday to rally Republicans behind J.D. Vance in a key Senate race. Two weeks earlier, he did the same for Mehmet Oz in Pennsylvania.

Neither candidate invited him.

Instead, aides to the former president simply informed the Senate campaigns that he was coming. Never mind that Mr. Trump, while viewed heroically by many Republicans, remains widely disliked among crucial swing voters.

The question of how to handle Mr. Trump has so bedeviled some Republican candidates for Senate that they have held private meetings about the best way to field the inevitable calls from his team, according to strategists familiar with the discussions.

This awkward state of affairs reflects the contortions many Republican candidates are going through as they leave primary season behind and pivot to the general election, when Democrats are trying to bind them to the former president.

In New Hampshire, Don Bolduc won the Republican Senate nomination on Tuesday after a primary campaign in which he unequivocally repeated Mr. Trump’s false claims of 2020 election fraud. Just two days later, he reversed himself, telling Fox News, “I want to be definitive on this: The election was not stolen.”

Some of Mr. Trump’s chosen candidates, after pasting his likeness across campaign literature and trumpeting his seal of approval in television ads during the primaries, are now distancing themselves, backtracking from his positions or scrubbing their websites of his name.

The moves reflect a complicated political calculus for Republican campaigns, which want to exploit the energy Mr. Trump elicits among his supporters — some of whom rarely show up to the polls unless it is to vote for him — without riling up the independent voters needed to win elections in battleground states.

In North Carolina, Bo Hines, a Republican House candidate who won his primary in May after proudly highlighting support from Mr. Trump, has deleted the former president’s name and image from his campaign site. A campaign official described the move as part of an overhaul of the website to prioritize issues that are important to general-election voters.

But Mr. Trump’s endorsement remains prominent on Mr. Hines’s social media accounts. Reached by phone, the 27-year-old candidate said he planned to attend a Trump rally in the state next week and then cut short the call.

In Wisconsin, Tim Michels, the Republican nominee for governor, erased from his campaign home page the fact that Mr. Trump had endorsed him — but then restored it after the change was reported, saying it had been a mistake.

“The optimal scenario for Republicans is for Trump to remain at arm’s length — supportive, but not in ways that overshadow the candidate or the contrast,” said Liam Donovan, a Republican strategist and a former top aide at the National Republican Senatorial Committee.

Mr. Donovan, as well as consultants and staff members working for Trump-backed Senate candidates, said the former president could be most helpful, if he chose, by providing support from his powerful fund-raising machine.

“A big part of the problem is that these nominees emerged from messy fields where the party has been slow to unify,” Mr. Donovan said. “But to fix what ails, what these G.O.P. candidates need isn’t a Trump rally, it’s a MAGA money bomb.”

Taylor Budowich, a spokesman for Mr. Trump, said in a statement that the former president’s “name and likeness was responsible for the unprecedented success of the G.O.P.’s small-dollar fund-raising programs,” and that he continued to “fuel and define the success of the Republican Party.”

Mr. Budowich added, “His rallies, which serve as the most powerful political weapon in American politics, bring out new voters and invaluable media attention.”

But linking arms with the former president could create problems for candidates in close races.

Even though he has been out of office for nearly 20 months, Mr. Trump has remained a constant presence in news headlines because of mounting criminal and congressional investigations into his role in the attack on the Capitol on Jan. 6, 2021, his refusal to hand over sensitive government documents that he took to his Florida home, and whether he and his family fraudulently inflated the value of their business assets.

On Thursday, when asked about the possibility of his being indicted in the document inquiry, Mr. Trump told a conservative radio host that there would be “problems in this country the likes of which perhaps we’ve never seen before.”

Polls suggest these controversies could be taking a toll. Among independent voters, 60 percent said they had an unfavorable view of Mr. Trump, compared with 37 percent who had a favorable view, according to a New York Times/Siena College poll released this week. President Biden was also underwater among these key voters, but by a far smaller margin of eight percentage points.

Asked whether Mr. Trump had “committed any serious federal crimes,” 62 percent of independent voters said they believed he had, and 53 percent said he had threatened American democracy with his actions after the 2020 election.

Republican candidates appear to be aware of such sentiments, backing away from Mr. Trump’s fixation on the 2020 election. While he has said that election fraud is the most important issue in the midterms, polls show that voters are far more worried about economic issues and abortion rights.

Three days after Mr. Trump’s rally in Pennsylvania, Dr. Oz, the Republican Senate nominee, told reporters that he would have defied the former president and voted to certify the 2020 presidential election.

Dr. Oz, a former TV personality, leaned on Mr. Trump’s endorsement to win a bitter primary. Since then, he has removed prominent mentions of the endorsement from his campaign website and has swapped out Trump-themed branding from his social media.

Republican campaigns said that they would not reject Mr. Trump’s help out of hand, but that accepting it created a whole set of other problems: Where, for instance, could a rally be held to energize the conservative base, while minimizing the damage among independents?

When Mr. Trump’s team called to say that the former president wanted to come back to Pennsylvania for a rally this month, Mr. Oz’s campaign guided him to Wilkes-Barre in Luzerne County. The county was one of three that voted twice for Barack Obama and flipped to Mr. Trump in 2016. It was also the only one of those three counties that backed Mr. Trump again in 2020. The other two — Erie and Northampton — supported Mr. Biden.

Mr. Trump’s rally in Ohio on Saturday will be his third visit to the state since leaving office — more than any other state so far. He twice won Ohio, a longtime presidential battleground, by eight percentage points.

This year, his endorsement of Mr. Vance’s Senate bid has been widely viewed as the clearest example of his enduring political influence. Mr. Vance, an author and venture capitalist, was trailing in the polls before Mr. Trump backed him with just over two weeks left in the race. Mr. Vance won the crowded primary by nearly 10 points.

For the rally on Saturday, Mr. Vance’s team directed the former president to Youngstown, a blue-collar area that had been a Democratic stronghold until Mr. Trump ran for president. The rally, at the 6,000-seat Covelli Centre, is also squarely in the congressional district represented by Tim Ryan, the Democrat running against Mr. Vance.

The event is scheduled to start at the same time as kickoff for an Ohio State University football game. Buckeyes games regularly draw huge statewide audiences, and the matchup on Saturday is against the University of Toledo, an in-state team.

The timing was not viewed as ideal by either Mr. Vance’s campaign or Mr. Trump’s team, and Mr. Trump was ultimately consulted on the decision, according to people familiar with the discussions. In the end, the two sides determined that it was more important to hold the rally on a Saturday night, when Mr. Trump has the easiest chance of drawing a strong crowd.

Ohio politicians have long tried to avoid competing for attention with Ohio State football games. In an interview, Mr. Ryan said holding a rally at the same time suggested that Mr. Vance — an Ohio State graduate — was out of touch with the “cultural things” important to Ohioans.

“It just says a lot,” Mr. Ryan said. “These little things just sometimes reveal a lot more about a candidate than it appears.”

In a statement, Mr. Vance called his rival “a radical liberal” and said, “The only person out of touch with Ohio is Tim Ryan.”

Mr. Ryan is also involved in a similar dance around the leadership of his party, given that Mr. Biden is himself struggling with low approval ratings.

Asked if he would campaign with the president this fall — even if it were not during a Buckeyes game — Mr. Ryan said: “No. Uh-uh.”