According to witnesses, some of Mr Cruz’s neighbours went out on to the street to watch the impromptu mariachi performance Sunday, which was organised by Adam Jama, from Carrollton, Texas.
Mr Jama wrote on a fundraising page for the mariachi band that “no one should go to Cancun and not listen to mariachi”, after Mr Cruz cancelled the planned trip.
The vacation – which was cancelled by Mr Cruz after touching down in Cancun on Thursday morning – came amid widespread power outages, and as thousands remained without running water for the fourth day running.
Mr Cruz admitted afterwards that the vacation was a “mistake”, and that he "was trying to take care of my kids,” who like millions of Texans last week, went for days without power.
“It's unfortunate, the fire storm that came from it. It was not my intention,” he told ABC13. “In saying yes to my daughters to somehow diminish all the Texans that were going through real hardship."
As criticism continued over the weekend, videos posted on Twitter on Sunday showed the mariachi band playing songs outside Mr Cruz’s home in Houston, Texas, as a form of protest against the senator’s actions.
“Senator Cruz, being an amazing dad, dropped off his family in Cancun in the middle of a major crisis and came back to Texas to continue serving his constituents,” wrote Mr Jama.
“We want to thank Senator Cruz for his leadership and pay for an amazing mariachi band to perform for him. No one should go to Cancun and not listen to mariachi,” the fundraiser added. All proceeds will go directly to Texas Children Hospital in Mr Cruz’s neighbourhood of Houston.
Temperatures reached as low as 0F (-18C) in Texas last Sunday, in what was the worst winter storm to strike the state in some three decades — and with as many as five million people thought to be without power at the worst point last week.
At least 30 fatalities have also been reported in weather-related incidents, leading to one bystander at the mariachi band protest holding a sign that said: “Cruz’s lies cost lives”.
Mr Cruz said in a written statement on Thursday: “"With school cancelled for the week, our girls asked to take a trip with friends. Wanting to be a good dad, I flew down with them last night and am flying back this afternoon."
Mr Cruz later told Fox News anchor Sean Hannity that “I had initially planned to stay through the weekend and to work remotely there, but as I – as I was heading down there, you know, I started to have second thoughts almost immediately because the crisis here in Texas, you need to be here on the ground."