At St. Paul United Methodist Church, one of this city’s oldest African American churches, fiery young pastor Richie Butler delivered a message last Sunday that hit home with the white woman sitting at the center of the second pew.

“Don’t get confused between success and significance,” Butler said. “This day! This is your moment! Don’t miss your moment!”

When Wendy Davis’s turn came to give her own testimony, she began, “Very fitting with your sermon today, pastor.”

For Davis, the Democratic gubernatorial nominee, success is looking all but out of reach. If there was a moment when she might have leveraged her national celebrity to break the Republicans’ 20-year lock on statewide office here, it appears to have passed. Davis has proven a disappointment as a candidate, and Democrats lament privately that her campaign has been a mess.

The question that remains to be answered on Election Day is more about significance: How much will Davis’s candidacy have done, along with other Democratic efforts, toward making her party truly competitive in Texas?

Texas has 38 electoral votes — second only to California’s 55 — and putting it into play would change the balance of the nation’s politics.

“It’s the question right now among people who are watching this stuff: Can the Democrats win by losing, and where is that line?” said James R. Henson, director of the Texas Politics Project at the University of Texas at Austin.

Recent public polls give Texas Attorney General Greg Abbott, the GOP nominee, a double-digit lead.

The latest bad news came Thursday, with a University of Texas/Texas Tribune survey that showed Abbott 16 points ahead of Davis. Her campaign noted that it was conducted over the Internet — regarded as less reliable than surveying through traditional interviews — and maintained that its internal numbers show the race is closer. But the Texas Tribune results are in line with a recent random-sample telephone survey sponsored by Houston Public Media and KHOU-TV, which also put Abbott 16 points ahead.

One benchmark, Henson said, is whether Davis will do significantly better than 2010 Democratic nominee Bill White, the Houston mayor who lost to incumbent Rick Perry by close to 13 points. If not, the results in November could undermine the idea that money and organization are the key to winning for Democrats in Texas.

The theory rests on rapid changes that are expected to make Latinos the largest demographic group in Texas within six years.

“Quite frankly, statewide races in the past have been very complacent about consistently having a program in those Latino communities,” said state Sen. Leticia Van de Putte, the Democrats’ nominee for lieutenant governor. “We haven’t had a race in two decades that has put resources into Latino communities. I am so proud of the strides we have made, but I wish there was so much more.”

Davis was an obscure state senator before she rose to fame with an unsuccessful filibuster against antiabortion legislation in 2013. She has proved to be a leaden, polarizing figure at the top of the ticket, starting with an early stumble over questions about whether she had embellished her hardscrabble biography. More recently, she drew national attention — and criticism — when she ran an attack ad against Abbott that featured the image of an empty wheelchair. Her opponent is paralyzed as the result of an accident; her campaign said the spot was an effective means of drawing attention to what it says is his hypocrisy when it comes to the plight of other victims.

Some Democrats grouse that Davis has become a drag on other party candidates — including Van de Putte, a Hispanic lawmaker who is popular with the business community.

Nonetheless, Davis has raised more than $30 million, a staggering amount of money for a Texas Democrat. Her star power was such that it brought in contributions from the likes of Barbra Streisand and Steven Spielberg. Abbott, however, retains a significant financial advantage, entering the final month of the campaign with about five times as much money on hand as Davis.

Davis also stands to benefit from the organizing efforts of Battleground Texas, a longer-term initiative that predates her campaign and that is sharing resources with it. The group was founded by Jeremy Bird, who directed the spectacularly successful field operation for President Obama’s 2012 reelection campaign.

Together, the two endeavors claim to have built an army of 32,000 volunteers and deputized 8,600 voter registrars. In Houston’s Harris County, they say Democrats have more staffers on the ground than the party counted in the entire state in 2010. They also have invested in state-of-the-art analytic tools and in updating voter files.

“Wendy wants to leave something behind” after the campaign is over, said one Davis aide who asked for anonymity because he was not authorized to speak for the campaign. “Battleground will continue to pick up the flag and move forward.”

Just having such resources is something new for Texas Democrats. “You see a light bulb go off in people’s heads. They start to hope,” said Byron Sanders, who was among a group of young Latino and African American professionals that met with Davis for lunch after the church service. “Whether she wins or loses, what we’ll start to see is the changes that the demographics of Texas have started to foretell. This changes the entire game, because people see this is not just an exercise in Democrats having to put [a token candidate] on the stage.”

Republicans see it the same way — despite Davis’s dismal prospects — which is one reason they often talk as though their real opponent this year is Battleground Texas.

“We need to strike a demoralizing blow to the Democrats. We need Greg Abbott to win by 15 to 20 points,” Robin Armstrong, a Republican national committeeman, said Wednesday at a meeting of the Bexar County Republican Women in San Antonio.

If Abbott wins big, Armstrong said in an interview, “the message is that the Democratic Party spent extraordinary resources in our state and they were unable to make a dent in our margins. That would send a huge message that their efforts have failed in Texas.”

Texas is notorious as a state with low voter turnout, and early indicators of who is likely to show up at the polls in this election are mixed. Battleground Texas touts that there are 300,000 more voters on the rolls than there were in 2012 — a record level of more than 14 million — reversing the typical trend in which registration drops after a presidential election year.

Whether that redounds to the benefit of the Democrats, however, is another question. The rate of growth in voter registration is more than a percentage point lower than the increase in the state’s population, said Ross Hunt, a partner with Murphy Nasica Associates, which does data analysis for Abbott’s campaign. And the bulk of that registration increase, he said, has occurred in parts of the state that lean conservative.

“It’s all smoke,” said Abbott adviser David Carney, who dismissed Battleground Texas as “a jobs program for Democratic consultants.”

Early voting began Monday, and initial signs are that it is more brisk than in the last gubernatorial election, and that could be a boost to Democrats. They have put heavy emphasis on banking votes in advance, especially in light of the state’s stringent voter-identification law.

“Our work is paying off,” Davis declared at a rally in Austin. That may well be true — somewhere down the road.

Alice Crites contributed to this report.