He is now the stuff of viral internet legend. After snow disrupted their flights, Will Hurd, the former Republican congressman, and Beto O’Rourke, a Democrat from a neighboring district, hopped into a rented Chevy Impala and took a cross-country road trip from their home state of Texas to Washington.

Broadcasting live what they called “a bipartisan town hall” to millions of Americans on Facebook and Twitter, complete with hour-long policy debates on health care, songs along to Willie Nelson and donut races, the two captured national attention as Americans watched. cultivate a friendshipeven when they disagreed.

More than six years later, on a sunny July day, Hurd was on the road again, this time as a longer-term presidential candidate, a moderate whose penchant for bipartisanship puts him at odds with the party’s current mood.

Traveling in a gray rented SUV and traversing New Hampshire’s wooded roads, he was seeking the spotlight once again, in a race for the Republican nomination that is being driven by some of the party’s strongest and most partisan voices.

“Have I changed my opinion that what unites us more than divides us? No,” Hurd said, recalling the lessons he learned from his trip with O’Rourke. “People were longing for something different, longing for it.”

Hurd, 45, wants to show voters that he brings something different to the race. A black Republican who has represented a majority Latino district and wants to broaden his party’s appeal is not about, as he puts it, “banning books” or “harassing my friends in the LGBTQ community.”

It’s a hard sell in a primary that has so far been dominated by culture war issues that are the focus of the main candidates, as well as legal issues surrounding former President Donald J. Trump.

Mr. Hurd has the most difficult of roads ahead of him. He has been on the campaign trail for just over a month and lags his opponents in personnel, name recognition and fundraising. The last quarterly filings showed that he had just $245,000 cash in hand.

He may not qualify for the first Republican primary debate on Aug. 23, which requires candidates to attract a minimum of 40,000 unique donors and at least 1 percent of voter support in three approved polls.

Even if he did meet those requirements, he still may not make it to the debate stage: He has refused to honor the Republican National Committee’s most disputed stipulation, that candidates sign a pledge to support their party’s eventual nominee. Not having a seat at the debate table means losing the most important lever to attract attention in the primaries.

At a pit stop outside Manchester, Hurd said he had no problem defending another Republican. But he said that he would not support Trump. “I’m not going to lie to get a microphone,” Hurd said, eating a Philly cheesesteak and salty fries.

Back on the road, Hurd didn’t downplay the challenges. At interviews, town halls and political events, he is often quick to refer to himself as a “dark horse” or “a start-up,” meticulously targeting the type of voter who the data suggests might be most open to his background and message. Those voters, he added, include a cross-section of people — Republicans, independents and moderates — who are tired of the toxicity in politics, reject Trump, and want someone with a vision for the future of the GOP. Demonstrating that this group of people actually exists as a coherent base of support will be the ultimate test of your candidacy.

Mr. Hurd’s charisma and enthusiasm for shaky politics comes through in one-on-one conversations, but it remains to be seen how well his experience will translate to the stump. At a 2024 presidential candidate speaker series at Dartmouth College, where he arrived that afternoon, an audience of more than 50 seemed to gradually warm to Hurd after a rocky start.

“We are in a competition: the Chinese government is trying to outdo us as a global superpower,” Hurd said, warning that AI could lead to unemployment but could also help bridge inequality in education. “And I am very specific. I mean, the Chinese government. It is not the Chinese people. It’s not Chinese culture. They are not Chinese Americans.”

At the hearing, Alice Werbel, 78, a retired nurse practitioner who drove from Norwich, a bedroom community in Vermont, said she saw Hurd as “promising” and praised him for his courage in refusing to sign the debate pledge.

But when Hurd’s comments wrapped up, she didn’t seem convinced he had a path to the presidency. She said that she planned to vote for President Biden in 2024.

“Biden should name him tech czar or artificial intelligence czar or cabinet tech secretary,” he added.

Later, at a dinner where Hurd spoke to a small group of students, Josh Paul, 21, a conservative and government student, wasn’t sure the Texas Republican could pull off a victory either, but said he was going to help Hurd try. He had found Hurd’s rejection of Trump so refreshing that he sought out a campaign staffer to sign up as a volunteer.

“I don’t understand how, if conservatism is about faithfulness to your oath and to the Constitution, how can you sit quietly while this guy lies and lies and lies and incites an insurrection,” Paul said, referring to Trump and the attack on the US Capitol on January 6, 2021.

During three terms, Mr. Hurd represented one of the most competitive constituencies in the country: a vast, largely Hispanic area stretching from El Paso, in the far west of Texas, along the country’s southwestern border, to San Antonio. Hurd, the only black Republican in the House when he announced his retirement in August 2019, said one of the reasons he was leaving Congress was to help diversify the ranks of his party.

Hurd has been a fierce and consistent critic of Trump, but has remained a staunch Republican with conservative values. Speaking to Dartmouth students, he said he would be willing to sign a 15-week ban on abortion, with exceptions for certain cases, such as rape or incest. Like his Republican rivals of color, he walks a thorny line between rejecting the existence of a system of racism in America and describing situations that seem to fit the definition.

On the road trip through New Hampshire, she said that when her parents first came to San Antonio, they had to live in the only neighborhood where an interracial couple could buy a home. “There are still some communities that don’t have equal opportunity,” she said. But, “I don’t know if I would call that systemic racism. I don’t call it that.

At a town hall Friday at Saint Anselm College in Goffstown, Thalia Floras, 60, a retail district manager and a swing Democrat, said her only concern with Hurd was her support for an abortion ban. However, she appreciated that he seemed open to hearing opposing views and did not resort to using phrases like “woke up the crowd” or “radical left.”

Marie Mulroy, 75, a retired freelance public health worker raised by a Republican mother and a Democratic father, said she had donated to Hurd because he was compassionate, liked working across the aisle and had “a better understanding of the world and where we’re going in the future.”

In any good political argument, he said, “you have to have the thesis, the antithesis, and the synthesis. But, “we no longer receive the synthesis,” he said. “And this is where the voters are: the voters are sitting on the synthesis.”