Asked what he admired about O'Rourke, Cruz managed to compare him to socialist Sen.
The candidates sparred as well over the embattled Supreme Court nomination of Brett Kavanaugh, who faces allegations that he assaulted a woman, Christine Blasey Ford, while both were in high school.
Such work would prove hard, Mr. Cruz said, given Mr. O'Rourke "has never talked to the president and wants to vote for impeachment".
Nonetheless, O'Rourke has raised significantly out-raised Cruz.
Sen. Ted Cruz speaks on a variety of topics at the Barn Door Steakhouse in Odessa, Texas, Aug. 25, 2018.
President Donald Trump has announced that he'll rally in Texas for his once bitter rival Cruz next month - previously unthinkable in a state where Republicans usually rack up landslide victories.
The hourlong debate at Southern Methodist University focused on domestic policy. Cruz called O'Rourke "out of step with Texas", and O'Rourke responded that "only one of us has been to each county in Texas". O'Rourke shouted out his "uncle Raymond", who taught him to shoot a firearm and was in law enforcement. The congressional district where the debate is located is represented by a Republican, Rep. Pete Sessions, but was won by Hillary Clinton by five points in the 2016 election.
"That's not true", Mr. O'Rourke rejoined, before expressing what he said were common sense moves Congress can make to ensure "weapons of war belong on the battlefield and not in public life". Democrats need to win a net total of two additional seats to take the Senate and 23 to assume the majority in the House. Texas has not elected a Democrat to the Senate since 1988.
O'Rourke's candidacy was once viewed as the longest of long shots. He also showed on screen, however, a recent Quinnipiac University poll that shows Cruz leading O'Rourke by nine points, 54 percent to 45 percent.
O'Rourke has built his campaign around healthcare, economic inequality, and resisting Trump and Cruz's immigration policies, as well as calling for some gun-control measures including uniform background checks and banning high-capacity weapons.