The Republicans who gathered at the Richard Nixon Presidential Library to watch their party’s presidential primary debate weren’t exactly spoiling for a fight. But they did want to see some policy disputes aired. They wanted some sign that maybe, just maybe, their party might move beyond former President Donald J. Trump.

Some said they got what they were looking for.

“They were almost all impressive,” Rocky Brister, 62, said on Wednesday night, standing over his empty wine glasses after watching the debate from a replica of the White House’s East Room.

“Vivek did great — boy, were they after him!” his wife, Loretta Brister, 61, added of Vivek Ramaswamy, the biotech entrepreneur who was a dominant force on the stage in Milwaukee. She said she hoped to see a Trump-Ramaswamy ticket.

Indeed, it was not that the roughly 200 Republicans who watched the debate from the shrine to the 37th president did not support the 45th. People in the crowd frequently referred to Mr. Trump as one of the greatest American presidents of all time. But many worried that his bombastic approach and criminal indictments had started to eclipse the policies he supported.

In a way, they were pining for the Republican Party of the past — eager to hear about fiscal conservatism, foreign policy and immigration, but from a candidate who could convincingly explain how to propel them into the future.

“I want to hear a vision, what they’re going to do to stop the country from going off the rails,” said Chuck Patton, 62, a retired sheriff’s deputy who came to the debate watch party with a group of neighbors, all lifelong California Republicans. “When we saw this Democratic president come in, we were angry, we were scared, but at this point we’re just going to let the Democratic cities just wallow in their misery.”

Depending on the view, the Nixon library is either a bizarre or an ideal place to take in a G.O.P. debate: a site dedicated to a Republican president who resigned in disgrace, broadcasting a showcase of candidates hoping to defeat a twice-impeached Republican former president who is facing four criminal indictments. Mr. Trump’s lead in the primary is so solid, he did not feel compelled to participate. (“Why should he?” Ms. Brister asked. “Anything he said would be used against him.”)

Orange County, home to the library and Nixon’s birthplace, remains California’s most reliable Republican stronghold, an important symbol in a state dominated by Democrats, and home to perennially competitive congressional districts.

Mr. Patton started the night convinced that one of the candidates could find a way to break free from the ever-present shadow of Mr. Trump, and left certain that many of them had. There was deep enthusiasm in the room for Gov. Ron DeSantis of Florida and Mr. Ramaswamy, even among voters who could not pronounce their names.

“It’s exciting — I’m an old guy, and I still like the young guys who are going out there hot,” Mr. Patton said.

Marla Robinson, a 62-year-old lawyer, had hardly given a thought to former Gov. Nikki Haley of South Carolina but was wowed by her performance, choking up as she described how inspired she felt by seeing a woman aggressively argue with a stage full of men.

Mr. Brister and Mr. Patton leaped to hoot and holler after Mr. Ramaswamy attacked former Gov. Chris Christie of New Jersey, an unrelenting Trump critic, by saying Mr. Christie’s campaign was “based on vengeance and grievance against one man.”

“The moderators are just trying to make him and Pence relevant,” Mr. Brister said, referring to Mr. Christie. “But it’s not going to happen, not a chance.”

Still, several Republicans said they were eager to see the party move on, in part because they feared the consequences if Mr. Trump is re-elected.

“He is just too divisive — there just are too many people on the left who hate that man,” said Dan Stow, 65, of Fullerton, Calif. “There is going to be too much turmoil and civil unrest if he is in office again,” he added, as others sitting around the table nodded in agreement.

Just before the debate began, the crowd sang “Happy Birthday” to former Gov. Pete Wilson of California, who ran for president himself and was on hand to offer his post-debate analysis. (There was no direct mention of his milestone age of 90.)

Mr. Wilson, who was widely blamed for a generational collapse of the state’s Republican Party after he supported an anti-immigrant ballot measure in the 1990s, offered a more pessimistic assessment of the night.

“Debates within your own party benefit the other side,” he said, adding that he was eager for visions about “bringing us back to the kind of America that we grew up in, at least I grew up in — but hell, I am the oldest one here.”

He tried to poll the crowd by asking them to applaud for the candidate they thought had won.

They offered polite clapping for Gov. Doug Burgum of North Dakota and Senator Tim Scott of South Carolina, and grew slightly louder for Ms. Haley, a former ambassador to the United Nations. Mr. Ramaswamy and Mr. DeSantis received raucous shouts. The more moderate candidates — Asa Hutchinson, a former Arkansas governor, and Mr. Christie — were met with silence.

Former Vice President Mike Pence, who has been reviled by some Trump supporters since he certified the 2020 election results, elicited hissing and boos.

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