So, what was he thinking? Tom Abrahams asked Cruz that question to kick off the sit-down interview and the senator said he was simply trying to be a dad. The high-profile Republican lawmaker told Eyewitness News he and his family were among the many Texans who lost power.
So his daughters mustered up an idea.
"They said, 'Look, let's take a trip. Let's go with some of our friends and let's get out of here and let's go somewhere warm," he recalled. "And [Cruz's wife Heidi] and I said ... let's go."
After his return to Houston, he quickly admitted that he regrets the decision to plan the getaway with his family. He told Eyewitness News he began feeling second thoughts the minute he sat down on the plane.
WATCH: Ted Cruz 'regrets' decision to take Mexico getaway during crisis
"You question what I was thinking, and ... I was trying to take care of my family," said Cruz. "I was trying to take care of my kids. It's unfortunate, the fire storm that came from it. It was not my intention. In saying yes to my daughters to somehow diminish all the Texans that were going through real hardship."
Cruz's office told ABC News the senator tested for COVID-19 Thursday morning to comply with mandates on traveling to the U.S.
Earlier in the day, the Associated Press reported Cruz went for a long-planned trip to Cancun and was expected to return almost immediately, according to a source with direct knowledge of the situation who spoke on the condition of anonymity to share private conversations. A source familiar with the senator's travel schedule told ABC News Cruz was scheduled to return to Texas on Saturday with his family.
The report, before Cruz's statement, only deepened when the Houston Police Department confirmed a member of the senator's staff contacted the department at Bush Intercontinental Airport on Wednesday to request assistance for Cruz's arrival.
"Upon Senator Cruz's arrival at Terminal E, HPD officers monitored his movements through the terminal," said Houston Police Chief Art Acevedo.
HPD was expected to escort Cruz once he arrives at the Houston airport, ABC News has learned.
The revelation opens Cruz, a key ally of former President Donald Trump, to fierce bipartisan criticism in Texas and beyond as he contemplates the possibility of a second presidential run in 2024. The two-term senator's current term expires in early 2025.
"That's something that he has to answer to his constituents about," state Republican Party Chairman Allen West said when asked whether Cruz's travel was appropriate while Texans are without power and water.
"I'm here trying to take care of my family and look after my friends and others that are still without power," West said. "That's my focus."
Hundreds of thousands of people in Texas woke up Thursday to a fourth day without power, and a water crisis was unfolding after winter storms wreaked havoc on the state's power grid and utilities.
Texas officials ordered 7 million people - one-quarter of the population of the nation's second-largest state - to boil tap water before drinking the water, after days of record low temperatures that damaged infrastructure and froze pipes.
In Austin, some hospitals faced a loss in water pressure and in some cases, heat.
Cruz's office has declined to release any details about the family vacation, but his staff reached out to the Houston Police Department on Wednesday afternoon to say the senator would be arriving at the airport, according to department spokeswoman Jodi Silva. She said officers "monitored his movements" while Cruz was at the airport.
Silva could not say whether such requests are typical for Cruz's travel or whether his staff has made a similar request for his return flight.
U.S. Capitol Police officials and the Senate Sergeant-at-Arms have encouraged lawmakers and their staff to be conscious of potential threats and to consider advising law enforcement about their travel at airports and other transportation hubs.
Cruz has been criticized by detractors on both sides of the political spectrum even before he ran for president in 2016. In more recent years, he has positioned himself as a Trump loyalist with an eye toward a potential second White House bid.
The Texas senator, who once described Trump as a "pathological liar," championed the-then president's call to block the certification last month of Democrat Joe Biden's election victory. That stand led to calls for Cruz's resignation after a violent mob stormed the Capitol as Congress was affirming Biden's win.
"Ted Cruz had already proven to be an enemy to our democracy by inciting an insurrection. Now, he is proving to be an enemy to our state by abandoning us in our greatest time of need," Texas Democratic Party Chair Gilberto Hinojosa said Thursday. "For the 21st time, the Texas Democratic Party calls on Ted Cruz to resign or be expelled from office."
Cruz's office dismissed calls for his resignation earlier in the month.
"The left - and some grifters on the right - are consumed by partisan anger and rage," his office said in a written statement. "Sen. Cruz will continue to work for 29 million Texans in the Senate."
The Associated Press contributed to this report.