The first-term senator holds a 3 percentage point edge over his Democratic challenger, Rep. Beto O'Rourke, according to a Quinnipiac poll released Wednesday. Forty-seven percent of Texas voters surveyed said they would support Cruz, while 44 percent said they would back O'Rourke, who represents the western edge of Texas.
The survey suggests Cruz will have to work to retain the Senate seat, which he won with more than 56 percent of the vote in 2012. Texas is one of the red states in which Democrats have mounted strong bids to unseat Republicans despite tough odds. Any gains in Republican strongholds would help Democrats reduce potential losses around the country as the party faces a daunting re-election map.
The race's dynamics still appear to favor Cruz. President Donald Trump won Texas by 9 percentage points in 2016, though Democrat Hillary Clinton outperformed President Barack Obama's 2012 showing in the state. Both Sen. John Cornyn, R-Tex., and Cruz breezed in their most recent elections in 2014 and 2012, respectively.
But Democratic enthusiasm and O'Rourke's fundraising prowess could put him in position to at least make the race competitive. In the first quarter, the O'Rourke campaign's staggering $6.7 million fundraising haul more than doubled the $3.2 million Cruz's campaign raised. Due to Cruz's previous money hauls, the two candidates ended March with about the same amount of cash on hand.
Cruz, 47, first won election in 2012 as a firebrand conservative opposed to the Affordable Care Act. He has largely aligned with Trump's priorities, supporting the GOP tax overhaul, tough restrictions on immigration and looser gun regulations.
O'Rourke, a 45-year-old who has served in the House since 2013, has tried to court progressives angered with the GOP agenda. He has sworn off funding from political action committees and backs policies such as Medicaid expansion in Texas and a path to citizenship for young immigrants brought to the U.S. illegally as children.
Republicans hope to keep or expand their narrow 51-seat majority in the Senate, as Democrats and independents who caucus with them defend 26 seats in November.
Here are some of the other findings from the Texas poll, which was taken from April 12 to April 17:
The telephone poll surveyed 1,029 Texas voters and has a margin of error of plus-or-minus 3.6 percentage points.
Graphic by CNBC's John Schoen