Most O'Rourke voters ranked healthcare as their most important issue, followed by the Supreme Court, while Cruz supporters chose the economy or immigration. Only 1 percent of those polled were undecided.
Democrat Beto O'Rourke released his first Spanish-language TV ad Tuesday, to go on air this week in eight Texas media markets, including Fort Worth.
Cruz leads O'Rourke among likely voters 54 to 45 percent. "These numbers may calm that talk".
The Reuter's poll defies a similar study released by Quinnipiac University on Tuesday that showed Cruz opening a wide 9-point advantage over O'Rourke.
The comments the group is referring to came at a different campaign even last week, when Cruz told a gathering of supports that liberals want Texas "to be just like California, right down to the tofu and silicon and dyed hair".
Cruz didn't explain what tofu has to do with O'Rourke or Democrats, or how a US senator would outlaw barbecue in a state, but in a speech a week earlier, he said liberals wanted to make Texas "just like California, right down to tofu and silicon and dyed hair".
Quinnipiac also found that Republican Gov. Greg Abbott holds a strong lead over his Democratic challenger, as well as having high favorability and job approval ratings.
"We are seeing tens of millions of dollars flooding into the state of Texas from liberals all over the country who desperately want to turn the state of Texas blue", Cruz said. Both polls surveyed likely voters in November's election.
Among the bright spots for Democrats: U.S. Representative Beto O'Rourke of Texas had a 2-percentage-point lead over Cruz among likely voters in the state and U.S. Representative Kyrsten Sinema of Arizona had a 3-point lead over Republican congresswoman Martha McSally in the race to succeed U.S. Senator Jeff Flake, one of Trump's most vocal critics from within his own party.