Texas senator Ted Cruz flew to Mexico with his family while the state he represents deals with power outages and water supply issues due to freezing temperatures.
Parts of Texas have been without power for four days, with hospitals facing a loss of water pressure and heat.
Meanwhile, the prominent Republican flew to the resort city of Cancun with his family.
In a statement, the senator said he was “wanting to be a good dad” by flying with his daughters as they went on a holiday while school was cancelled and the power was out – adding that he was flying back on Thursday afternoon.
Mr Cruz ran to be his party’s presidential candidate in 2016, but was defeated by Donald Trump.
There is speculation he may try to run again in 2024, with his current term as senator expiring in early 2025.
There has been criticism of Mr Cruz’s travels by the Democrats.
Houston police confirmed officers provided assistance to Mr Cruz as he travelled through the city’s airport.
A spokesman said: “They reached out to us, let us know that he was going to be arriving and could we assist, so upon his arrival to the Houston airport we monitored his movements.”
Mr Cruz said in a statement: “This has been an infuriating week for Texans. The greatest state in the greatest country in the world has been without power.
“We have food lines, gas lines, and people sleeping at the neighbours’ houses. Our homes are freezing and our lights are out. Like millions of Texans, our family lost heat and power too.
“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.
“My staff and I are in constant communication with state and local leaders to get to the bottom of what happened in Texas.
“We want our power back, our water on, and our homes warm. My team and I will continue using all our resources to keep Texans informed and safe.”
Texas, in the south of the US, is known to occasionally get flurries of snow – but recent days have seen incredibly cold temperatures in the second largest state in the country.
Seven million people have been told to boil water before drinking it, after water infrastructure was damaged by the low temperatures.
Hospitals in Austin are facing a loss of water pressure and in some instances heat.
Mr Cruz was one of the leading voices in calling for Congress to block the certification of Joe Biden’s electoral victory before the 6 January riots.
Calls were made for Mr Cruz to resign after the unrest.
On Thursday, the chair of the Texas Democratic Party, Gilberto Hinojosa, said: “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.
“For the 21st time, the Texas Democratic Party calls on Ted Cruz to resign or be expelled from office.”