Rep. Chip Roy, R-Texas, held Democrats responsible for the ongoing crisis at the southern border, but warned that his own party and its leadership will be on the hook if they agree to give the Biden administration a "blank" check in an omnibus bill this week without taking measures to secure the border.

In a "WHD News Sunday" interview, Roy accused Democrats of wanting "to simply throw more money at the border and then process more human beings while they’re getting abused," and that by giving the administration more money via an omnibus bill, it will only continue the problem.

"We’ve been running on this being the Biden border crisis," Roy told host Shannon Bream. "This the McConnell-Republican border crisis if we give them more money this week without demanding that they secure the border, and do more bloated spending and giving DHS money with a blank check."

As part of the omnibus bill that lawmakers from both parties are hoping will fund the government going forward and avoid a shutdown, the Biden administration is requesting a $3.5 billion increase from last year for managing border. The overall cost of the omnibus is expected to be roughly $1.65 trillion.

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Earlier in the program, Rep. Veronica Escobar, D-Texas, acknowledged that there "absolutely" is a problem but claimed that Republicans were making it worse by repeatedly saying that there are open borders.

Roy scoffed at that, saying that he and fellow Republicans in Texas are "actually trying to solve the problem," citing a Texas Border Plan that he and colleagues have developed.

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"We know what to do," he said. "We saw it work under the Trump administration, but it's also common sense." He said that there has to be both the infrastructure – like building roads and a border wall  – as well as policies to "turn away and detain" instead of "apprehend and release."

Roy also brought up a 2018 bill from Republicans that he said would have granted benefits to recipients of the Deferred Action for Childhood Arrivals (DACA) program while securing the border and putting in place additional immigration reforms – but no Democrats voted for it.

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The Biden administration insists that it has policies to address the border, with Homeland Security Secretary Alejandro Mayorkas touting a six-point plan. Roy said that plan is just "a supercharged apprehend and release.