Senator Cruz is still facing a single-digit re-election race, according to a new poll. 

A University of Texas/Texas Politics Project poll shows Mr. Cruz leading Congressman Colin Allred 51 percent to 44 percent. It also finds that voters have a more favorable view of Mr. Cruz than his Democratic challenger, who has less name recognition. 

The survey comes as the race has become one of the few Democrats feel optimistic about flipping as they are defending several Senate seats this year.

Earlier this month, the election forecaster, the Cook Political Report, downgraded its standing for the Texas senator in the race to the less favorable “lean Republican” from “likely Republican.” And RealClearPolitics’ average of polls finds Mr. Cruz has a 4.5 percent lead over Mr. Allred.

The single-digit polling, with some showing Mr. Allred in the lead, has led Democrats to pour millions of dollars into the race in the hope of defeating the incumbent Republican.

Democrats are also spending heavily in Florida, where they think they have a shot of unseating a Republican incumbent senator, Rick Scott. Last month, the Democratic Senatorial Campaign Committee said it was making a “multimillion-dollar” ad buy in the two states. 

The DSCC chairman, Senator Peters, said in a statement about the ad campaign, “Senate Democrats are expanding the map and going on offense.”

“All cycle long, the DSCC has been preparing to take advantage of Sens. Cruz and Scott’s damaged standings in their states — and now our efforts in Texas and Florida are accelerating,” he added. 

While Democrats are hopeful about their chances of winning in Texas, it is not the first time in Mr. Cruz’s Senate career he faced a close race. In 2018, he ran against Congressman Beto O’Rourke.

The Texas Politics Project noted that in its October 2018 poll, Mr. Cruz led Mr. O’Rourke 51 percent to 45 percent and won the race 50.9 to 48.3 percent. 

Six years later, some of the dynamics regarding where the two candidates are drawing their support remain the same. However, the latest Texas Politics Project poll finds the Republican senator is only trailing Mr. Allred in urban areas by five points, a significant narrowing of the gap from 2018 when he trailed Mr. O’Rourke by more than 30 points. 

Additionally, the latest poll finds Mr. Cruz and Mr. Allred are statistically tied among Hispanic voters. In 2019, Mr. O’Rourke held a nearly 30-point lead in that demographic.

The Texas Politics Project poll is the second survey this week to show Mr. Cruz expanding his lead. A University of Houston poll released on Wednesday found him leading Mr. Allred by four percentage points, up from two percentage points in August.