The debate begins at 6 p.m.at Southern Methodist University in Dallas and is the first of three hour-long debates between the two Texas candidates.
"I did not try to leave the scene of the accident, though driving drunk, which I did, is a awful mistake for which there is no excuse or justification or defense", O'Rourke said.
O'Rourke, a charismatic congressman from El Paso, has benefited from an avalanche of media attention and a gusher of small donations, raising millions of dollars more than Cruz. 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".
On the topic of President Trump, Cruz said O'Rourke wants to impeach the president.
O'Rourke denied that and offered another confrontational retort as Cruz challenged him to name a judge he has supported who would defend the Second Amendment. I'm sorry that you don't like thoughts and prayers. He said the incident led him to fight to eliminate racial biases from the criminal justice system and help those who have served their time get jobs.
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.
"I could have chosen to make it about myself, to be selfish and say, you know what, my feelings are hurt, so I'm going to take my marbles and go home", he said.
The incumbent also criticized O'Rourke's past support for legalizing marijuana, evoking his older half-sister, Miriam, who died of a drug overdose.
But Nelson is taking some heat from conservative country music fans in Texas who can't understand why he is performing a fundraising concert for a Democrat.More news: Israel to present findings in Moscow over downing of Russian plane
Such work would prove hard, Mr. Cruz said, given Mr. O'Rourke "has never talked to the president and wants to vote for impeachment".
Belatedly, Texas Republicans have realized O'Rourke poses a serious threat, but their efforts to beat him back have so far been strangely off the mark.
The element that Cruz considers damning is O'Rourke campaigning against police injustice (even a very clear one) before a heavily-black audience.
"Hold on, more armed police in schools is not thoughts and prayers".
In the debate, the two candidates clashed over issues such as immigration, gun rights, trade, and protests of the National Anthem, with O'Rourke frequently complaining that Cruz was misrepresenting his positions.
So why such a big difference in these two polls?
The moderator wrapped up the debate by asking both Senate candidates to say something they "admire" about the other, which similarly took place during the second presidential debate between Donald Trump and Hillary Clinton in 2016.
Cruz offered no compromise on hardline immigration measures or gun control, months after a mass shooting at a high school near Houston.