"The DHS press release is over the top. It's poisonous. I think its ridiculous and I've long since stopped paying attention to them," he said.

Graham added that any time the department is offered money for the border wall they should "say thank you."

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DHS ripped a deal offered by a bipartisan coalition of senators, saying it "destroys" the department's ability to remove undocumented immigrants from the country and "ignores the lessons" of Sept. 11, 2001.

"It would be the end of immigration enforcement in America and only serve to draw millions more illegal aliens with no way to remove them," the statement said. "By halting immigration enforcement for all aliens who arrived before June 2018, it ignores the lessons of 9/11 and significantly increases the risk of crime and terrorism."

The proposal crafted by the senators would allow about 1.8 million immigrants brought to the United States illegally as children to stay with a path to citizenship. It also provides $25 billion for border security and would impose limited changes to family-based immigration.

But it doesn't include broader changes to family-based immigration, which conservatives call "chain migration," or eliminate the State Department's diversity visa lottery.

“I don’t think the staffers who compiled this document served the President very well. As for Secretary Nielsen, I’m incredibly disappointed in her for allowing her office to become so politicized and for allowing something like this to go out," he added.