Former President Donald Trump is claimed to have made shocking comments about migrant children on Truth Social.
Greene said the "enemy" was Mexican cartels: "not the Mexican government, not the Mexican people."
The Texas governor has blamed an influx of migrants at the southern border of the Lone Star State on U.S. President Joe Biden.
"I think that there is a good bet that somebody that's come across that [Southern] border will commit an act of terrorism," the Florida governor said.
Carlson said the Republican governor of Texas had not done anything "meaningful" to secure the southern border.
The Republican governor said Texas will appeal a federal judge's ruling ordering the state to remove the Rio Grande floating barrier.
"I don't see an ending to this," New York City's mayor said, adding that 10,000 migrants are arriving in the city every month.
The state must remove floating border buoys by September 15, a federal judge said in a ruling criticizing Governor Greg Abbott for ignoring federal law.
The migrants were exposed to the elements, including rain, early Tuesday morning in Starr County, Texas.
Nearly $500,000 worth of materials intended for construction of the wall have been sold since late July.
Hilary is hurtling toward Mexico's Baja California peninsula as a Category 1 hurricane and is expected to hit California as a tropical storm.
The Florida governor on Friday discussed a new proposed tax on money sent by migrants back to Mexico, which he said would fund a border wall.
DeSantis has made aggressive promises about the U.S.-Mexico border if he is elected president.
"It's hard to fault Senator Sinema's criticism," strategist Jay Townsend told Newsweek. "It would be hard to fault candidate Gallego if he joins the chorus."
Sylvia Garcia, a Democrat, said the materials "are meant to inflect physical harm to asylum seekers."
One Democratic strategist said that the Texas governor "shouldn't be sued, he should be prosecuted" over his treatment of migrants.
Approximately 1,000 feet of the barrier was installed on the Rio Grande, costing Texas $1 million.
Mexico's foreign affairs ministry has said the barrier, for deterring migrants, infringes upon established treaties governing river usage.
Rep. Sylvia Garcia said she was appalled by the "ongoing cruel and inhumane tactics" employed by Texas Gov. Greg Abbott at the southern border.
The Texas Republican governor was accused of participating in a "pathetic exercise in scoring political points at the expense of vulnerable people."
U.S. Customs and Border Protection reported that June saw the lowest number of migrant crossings at the Southwest border since February 2021.
Trump touted the idea after saying that ranchers in Texas were being allowed to open doors in the border wall, according to an upcoming book.
Republicans have scrutinized data about migrant children but the story behind it is complex.
The GOP congresswoman said the unrest was the result of immigration policy, warning of similar protests at home if there isn't more action on the border.