But political analysts say Mr. O’Rourke’s chances are a long-shot at best, despite his fund-raising skills. He remains unknown to many voters, even as he has kept up a hectic travel schedule and visited 228 of the state’s 254 counties. In the Democratic primary last month, Mr. O’Rourke lost a number of counties to two lesser-known Democratic rivals, including the Hispanic-dominated border area of the Rio Grande Valley, parts of East Texas and the northern Panhandle region.
On Monday, Mr. Cruz formally began his re-election campaign at a venue that has become one of his favorite political backdrops — the Redneck Country Club in Stafford, 17 miles southwest of downtown Houston. His speech and his surroundings were plastered with references to his new campaign slogan: “Tough as Texas.” It is meant to evoke the resilience of the state as it reeled from and united in the aftermath of Hurricane Harvey.
At a campaign event on Tuesday night in San Antonio, Mr. Cruz acknowledged Mr. O’Rourke’s success in fund-raising and the challenge for Republicans this November.
“That’s a whole lotta money — there’s no doubt about that — and it has been clear for some time that the hard left is energized and they’re mobilized and they’re angry at the president,” Mr. Cruz said, according to The Texas Tribune. “And we are seeing all across the country, the far left giving millions of dollars to liberal Democrats running for office, and it underscores that Republicans cannot take November for granted.”
Mr. Cruz remains popular with Texas conservatives, particularly the Tea Party activists who helped him, back in 2012, clinch the Senate seat by defeating one of the most powerful Republicans in Texas, David Dewhurst, then the lieutenant governor. And Republicans continue to dominate Texas, culturally and politically, controlling both chambers of the Texas Legislature, the governor’s mansion and all of the more than two dozen statewide-elected offices. Democrats have not won any statewide offices since 1994.
“Cruz has built-in name identification, conservative credentials and an ‘R’ behind his name, so his candidacy was effectively born on third base,” said Brandon Rottinghaus, a professor of political science at the University of Houston. “These advantages give him a serious head start, but he doesn’t want to be the hare who naps while the tortoise passes him by. O’Rourke’s fund-raising should be an eye opener for Senator Cruz.”
Texas Democrats have been in this position before. In 2014, Democrats had believed that Wendy Davis would become the first Democratic governor in decades, but Ms. Davis lost and Greg Abbott won. In 2016, Democrats had believed that Hillary Clinton could win Texas in the presidential race, but she lost and Donald Trump won the state.
The issue often comes down to voter turnout. In last month’s primary elections, Democrats surged to the polls in record-breaking numbers. More Democrats voted early this year than voted early in the presidential election year of 2016. In the end, though, they were still outvoted: A total of 1.5 million votes were cast by Texas Republicans in the primary, compared to 1 million by Democrats.
“Right now, history and recent elections are still on Ted Cruz’s side, and the dynamics of this state are still on Ted Cruz’s side, for Republicans to win at a statewide election from the governor’s office to senator and on down,” said Ted Delisi, a Republican strategist in Austin who was the national field director for former Gov. Rick Perry’s 2012 presidential campaign.
At an event in Waco on Tuesday, Mr. O’Rourke suggested to The Texas Tribune that one of the differences between his race and Ms. Davis’s failed bid for governor in 2014 was the backlash against the Trump White House. “She did not have the benefit of this year, where, I hope you’ll agree, we’ve never seen this level of urgency, this level of motivation,” Mr. O’Rourke said.
Asked if he was running against Mr. Cruz or Mr. Trump, Mr. O’Rourke replied, “Neither.” He added: “I’m not running against anybody. That just doesn’t get me going. It doesn’t energize me.”
Mr. O’Rourke’s fund-raising success is an outgrowth of a campaign driven by social media, which has refused to accept money from political action committees.
Republicans say they are not worried about an upset but are certainly paying attention. They point to the 2002 race for governor, when the Democrat, Tony Sanchez, a Laredo oil executive, spent $67 million and lost to Mr. Perry. They said that Mr. Cruz’s reputation among Texas conservatives took a knock in 2016 after he refused to endorse Mr. Trump at the Republican National Convention, but that Mr. Cruz had largely repaired the damage.
“I think he’s recovered from that,” said State Senator Paul Bettencourt, a Houston Republican who is a former treasurer of the Republican Party of Texas and who is supporting Mr. Cruz. “This is an unusual year. The electorate is roiled. Statewide, Republicans are going to have to take these races seriously and campaign accordingly.”
On Monday, Mr. Cruz and Mr. O’Rourke jabbed at each other on social media. Mr. O’Rourke’s campaign posted a Snapchat filter of a Cruz event in Beaumont and took a swipe at Mr. Cruz’s failed presidential run. “Ted Cruz visited 99 of Iowa’s 99 counties,” read the filter, which included an image of a frowning Mr. Cruz. “When’s the last time he listened to Texans in Beaumont?”
But Mr. Cruz wasn’t taking the bait. He responded on Twitter, saying he had been to the city four times in the past year while pointing out Mr. O’Rourke’s failure to win Jefferson County, which includes Beaumont, in the Democratic primary. “As best I can tell, you’ve been there once for a drive-by campaign event on Feb 9,” Mr. Cruz wrote on Twitter of Mr. O’Rourke. “Maybe that’s why you lost Jefferson County in the Dem primary.”
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