"There are places on the border where there's not even any security. I'm asking for [Mayorkas] to resign immediately. He doesn't tell the truth. If you don't think our country is in crisis and all you got to do is see a thousand people rush the border, and they come across. They used to come across in the dark. Now they come across in the daylight."

Videos taken at the Paso Del Norte bridge linking Mexico and the U.S. showed migrants of all ages pressing toward the fenced border, with some putting their hands in the air to encourage others to continue moving forward. The efforts were ultimately thwarted, according to border sources.

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Jones warned the country is in crisis as the U.S. is "being invaded." 

"There are 171 countries that come through Mexico and the United States. 171 different countries. They catch them from China. They come from Russia… We're being invaded. For them to stand up and say the border is in great shape, they're lying to each and every one of us." 

Jones said the U.S. needs to go after the drug cartels in Mexico because the Mexican government is too corrupt to do anything about them.

"Our military needs to be involved and go into Mexico. We need to defend our country right now. And if that means the military has to go into Mexico, we should look at that. And we've got to stop this. 100,000 people die of fentanyl poisoning in the United States every single year. And that number is going up." 

Rep. Nancy Mace, R-S.C., joined the fierce criticism of Mayorkas, Monday. 

"Our border is not secure," Mace told "Fox & Friends First." "Secretary Mayorkas is like a firefighter running away from a fire. He ought to be impeached for this. And this lawlessness has to end. This is unbelievable. They're putting the lives of our Border Patrol at risk here by allowing this kind of thing to happen. We're not following our laws. We allow them to come here illegally and stay here illegally without consequence. And you're seeing the results of that today."

"Secretary Mayorkas has buried his head in the sand," she continued. "I wish that we could impeach him for the crappy job he's clearly doing about the border."

There were more than 2.3 million migrant encounters in FY 2022 with FY 2023 on pace to top that record number.

Fox News' Bill Wehner and Bill Melugin contributed to this report