The poll found white voters back Cruz by almost two-thirds but O'Rourke leads by 78 percent among black voters. O'Rourke is projected to receive a larger percentage of female, black, Latino, young and independent voters, according to the poll.
That difference falls within the poll's margin of error.
Democrats are targeting Cruz in the November congressional elections "and they may be hitting the mark", Peter A. Brown, assistant editor of the poll, said in a statement. O'Rourke reported collecting $6.7 million in donations through March.
In the Texas governor's race, Republican incumbent Gov. Greg Abbott tops former Dallas County Sheriff Lupe Valdez 49 - 40 percent and leads entrepreneur Andrew White 48 - 41 percent. He holds a slight edge among women with 47 percent support to Cruz's 43 percent.
Cruz's favorability rating showed a polarized response: 46 percent of Texans have a favorable view of the senator while 44 percent have an unfavorable view. But in a state where Democrats haven't won a statewide election since 1996, does the El Paso congressman actually have a shot at knocking off Cruz? But 43 percent of Texas voters said Trump won't be an important factor in their choice for the Senate.
O'Rourke has spoken out repeatedly against President Trump's proposal for a border wall between the US and Mexico. "Voters disapprove 52 - 43 percent of the job President Donald Trump is doing" ... in Texas. He's best known for helping to spark a funding standoff in 2013 that led to a partial government shutdown, and working as a lead opponent to Obamacare.
Rep. Beto O'Rourke (D-TX) gives a speech alongside his wife Amy Hoover Sanders during a fundraiser baseball game on April 14, 2018 in Austin, Texas. His voting record largely aligns with most House Democrats. But when voters were asked which candidate they thought would do a better job on specific - the economy, taxes, healthcare, immigration, and gun policy - voters consistently favored Cruz.