When asked if he was anxious about an anti-Trump backlash in Texas that could affect him in the general election against O'Rourke, Cruz said he wasn't.
But he'll face a stiff challenge from Cruz, who released an attack ad jingle immediately after O'Rourke's primary win was solidified that insinuates he is pandering to Hispanics by using the name "Beto" instead of his birth name, Robert.
CNN's Chris Cuomo confronted Cruz about the snarky lyrics on Tuesday night.
However, the Republican senator also goes by a different name than his given name, Rafael Edward Cruz. He went the other way and has a more ethnic version of his name-why go after him?
Mr. Cruz told "New Day" on CNN: "In terms of the jingle, some of it is just having a sense of humor". My name is Rafael Edward Cruz.
O'Rourke said he has gone by Beto since he was born, telling the news outlet that "its kind of a nickname for Robert in El Paso".
O'Rourke, who is white, has said before that his parents began calling him Beto when he was a child.
While he easily won his party's senate primary with almost 62 percent of the Democratic vote and his mostly Hispanic El Paso district by more than 90 percent, O'Rourke struggled in certain regions, particularly the Rio Grande Valley. Texas's growing Latino population has been shifting the Lone Star State to the left.
"We can get into name-calling and talk about why the other person is such an bad guy, or we can focus on the big things that we want to do for the future of our country, for the generations that will succeed us", he said.
Nonetheless, O'Rourke will now seek to become the first Democratic senator from Texas since former Sen. He said Texas voters were far more interested in discussing jobs, health care and immigration.
Mr. O'Rourke has been raising more money than Mr. Cruz in recent quarters and has tried to awaken a dormant Democratic vote in rural parts of Texas by relentlessly holding town hall-style meetings. His congressional district is 75 percent Hispanic, and he openly opposes Trump's border wall.