BEAUMONT, Texas — Operating on two hours’ sleep, Beto O’Rourke was 20 hours into his day and looked it. His white shirt and gray slacks were an accordion of wrinkles. His hair, flecked with gray, drooped on his forehead and small dark rings had formed under his eyes.
But he hadn’t lost his voice. The Democratic congressman from El Paso was speaking to a crowd of several hundred at Suga’s restaurant, 830 miles from home, trying to make an improbable case: that he can defeat Texas’s incumbent Republican senator, Ted Cruz.
Democrats need to pick up two seats in the midterm elections to win control of the Senate, but they also must defend incumbents in 10 states that President Trump won. Mr. Cruz is seen as safer than, say, Dean Heller, Nevada’s Republican senator, or the seats in Arizona and Tennessee that are being vacated by incumbents. And with Democratic money playing defense for incumbents in Missouri, Indiana, West Virginia and elsewhere, Mr. O’Rourke expects no cavalry from Washington to come help him.
But Democrats will need wins wherever they can get them — so the long-shot is going it alone.
Mr. O’Rourke told the crowd at Suga’s that the “Dreamers” — young immigrants brought to the country illegally as children — should be protected. No wall should be built on the border with a friendly country. College must be more affordable. Women deserve access to reproductive health services. All Muslims should not be banned, and the press is not the enemy of the people.
He appealed to their sense of virtue. “This smallness, this bigotry, this paranoia, this anxiety,” he said, cadence accelerating, “we’ve got to be for the big, aspirational, ambitious things.”
He appealed to their sense of humor. “There’s a reason that Congress has an approval rating of around nine percent. Nine percent! Communism ten percent. Gonorrhea eight percent. We’re right in the middle.”
And he appealed to their anger at Washington. The “system is rigged,” he said, adding, “I can tell you that access is purchased, that votes are bought and paid for, that outcomes are determined before you have a chance to call your member of Congress or senator.”
The crowd cheered, they hooted, they left saying things like “he was great” and “I’m in.”
Before Beaumont, Mr. O’Rourke spoke to town halls this month in Lufkin and Woodville, deeply conservative places where Democrats are rarely seen. “It takes guts to come to this area,” one woman in Woodville said. The man who introduced him in Lufkin had just one request, that he refrain from swearing, an admonition that Mr. O’Rourke heeded in Lufkin but not in Beaumont.
Mr. O’Rourke is favored to win his party primary next month and challenge Mr. Cruz. But his odds in November are beyond long. No Democrat has won a statewide office in Texas since 1994, the year before Amazon sold its first book.
By the calculations of Mike Baselice, a Republican pollster in Austin, demographic changes might make Texas competitive in 2032, certainly not in 2018. Mr. O’Rourke’s quest, he said, is “same book, different chapter” of other Democratic hopefuls. “This is not a level playing field here.”
It has been so bleak for Democrats in Texas that they define victory in terms of the size of their losses. A running joke in Mr. O’Rourke’s speeches is that he has almost convinced his mother, Melissa, a Republican, to vote for him.
If the hill weren’t steep enough, Mr. O’Rourke also has refused to hire outside consultants or pollsters, and he will only accept contributions from individuals. He has no interest in using big data. When he tells this to Democratic colleagues in the House, some have simply turned and walked away from him, unable to take him seriously.
But there is power in the giant-killer narrative and signs that his anti-campaign playbook campaign is working. He raised $2.4 million in the last quarter, and gets applause when he notes that was $500,000 more than Mr. Cruz took in.
He has a restless energy that has put him in 217 of Texas 254 counties, driving tens of thousands of miles, fueled by bad coffee and Hostess cupcakes that supporters bring him.
In Lufkin, he was greeted with chants of “Beto, Beto, Beto.” His campaign took in $1,258 in checks and cash dropped into a large jar.
“I think he can win. I think he can inspire Texans,” said Susan McCulley, adding, “we’re not just mad, we’re scared.”
Another supporter, Ferryn Martin, said, “In 2010, the Tea Party was mad. This year, we are mad.”
Mr. O’Rourke tries to tap into that emotion. He livestreams almost every aspect of his campaign — the coffees, the town halls, “bowling with Beto,” stops at Whataburger, the drives between stops, which often include calls to voters and activists and from his wife, Amy. Driving with his left forearm and right elbow on the steering wheel, he asked her about the science fair projects of their three children.
His theory of the case is that he can make the sale in rural Texas in part simply by showing up. If he can cut down Mr. Cruz’s margins there and generate energy in urban precincts and suburbs, he can become the first Democrat since Lloyd Bentsen in 1988 to win a Texas Senate seat.
Democrats in Texas have long been saying that the demographic changes sweeping the state, fueled by a surge in the Latino population, would eventually make the state two-party competitive, but even some of the more optimistic forecasts don’t have that happening until 2024. Still, there are other factors at work that add to their hopes. The number of college-educated residents in the state increased by 20 percent from 2006 to 2016, according to Lloyd Potter, the Texas state demographer. Rural areas are losing population while urban and suburban areas are gaining.
“If one was able to figure out how to turn out the Latino vote and the African-American vote, that could change things pretty dramatically,” Mr. Potter said. “The issue is how far-off in the horizon it is.”
But President Trump, who carried by stated by nine percentage points, is complicating conventional analysis. “All things being equal, if there wasn’t a Trump, it would be in the mid 2020s until the state would get competitive,” said Russ Tidwell, a Democratic consultant who has worked in the state for decades. “But Trump makes other things possible.”
And Mr. O’Rourke’s campaign is all about a sense of the possible.
His biography does not have any of the bootstraps appeal of a Lyndon Johnson, or even Mr. Cruz, the son of immigrant parents. Mr. O’Rourke’s family was well-to-do in El Paso. Born Robert Francis O’Rourke, he has been known as “Beto” from infancy. His voice shows no hint of a Texas accent until his says his first name and sounds like he is speaking Spanish — which he does, fluently.
He was sent to Woodberry Forest boarding school in Virginia, then Columbia, where he was captain of the crew team. He played in a punk rock band, hauled expensive art and enjoyed the wanderlust that a young man from a wealthy family can afford. He went back to El Paso and started a technology company, then ran for City Council before winning his House seat in 2012, defeating an incumbent.
In the House, he has hardly left a footprint. He did not vote for Representative Nancy Pelosi to be the Democratic leader, and Mr. O’Rourke, 45, thinks his party in Congress needs fresh leaders, which is one reason he supports term limits.
Mr. Cruz, who did not respond to a request to discuss the race, has never been as popular as Republicans like former governors George W. Bush or Rick Perry, but he has been tactically adroit and plays well to more conservative voters. He has an uneasy alliance with Mr. Trump that started with the president calling him “Lyin’ Ted” during the primaries and has evolved into invitations to the White House.
Mr. O’Rourke’s is an emotive approach, Mr. Cruz’s one of cold-eyed precision.
“I don’t think he is a flash in the pan,” William Martin, a scholar at the Baker Institute at Rice University said of Mr. O’Rourke. “He’s young and fresh, and he’s just intrinsically so much more attractive than Ted Cruz for voters who don’t already have their minds made up.”
Mr. O’Rourke knows Mr. Cruz is a skilled debater, a proven fund-raiser and a candidate who showed in his presidential campaign that he could leverage analytics into millions of votes. And the congressman has vulnerabilities. Mr. O’Rourke has been arrested twice, once for a college prank, a second time, in 1998, for what he called the “unforgivably” bad decision to drive after “having too much to drink.” Both charges were dismissed.
His mother receives fund-raising solicitations from Mr. Cruz, who calls her son a “Nancy Pelosi liberal,” no doubt a preview of things to come.
But Mr. O’Rourke also will use Mr. Cruz’s well-observed ambition against him, and said that the incumbent’s real goal is another White House run. He cites a letter that Mr. Cruz sent to Gov. Kim Reynolds, Republican of Iowa, talking about visiting all of Iowa’s 99 counties.
“I know he hasn’t been to all 254 of Texas’ counties,” Mr. O’Rourke said.
Texas is so vast that it is nearly impossible to travel the entire state the way that Mr. O’Rourke has chosen to, largely by car, over state highways and rural roads, but he seems undeterred and drives most of the miles himself, with aides in passenger seats.
Over lunch at the Lufkin BBQ, Mr. O’Rourke said his campaign strategy was in part drawn from the 1968 presidential campaign of his political hero, Robert F. Kennedy, long on hope and aspiration.
Mr. Kennedy was not driven by “polls or consultants, but he really seemed to be grounded in the things that he found important,” he said, adding that he often seemed to be going directly against the advice of what was going to be popular.
Those seemed to be the words of a long-shot, a candidate with nothing to lose.