President Donald Trump is getting hit with blowback from his own party for his shake-up of the leadership at the Department of Homeland Security.

After the departures of the heads of Homeland Security and the Secret Service, Sen. Chuck Grassley, R-Iowa, urged Trump not to dump Lee Francis Cissna, the head of Citizenship and Immigration Services, who is also rumored to be on the chopping block.

And Grassley criticized the influence of White House adviser and immigration hard-liner Stephen Miller, noting that Miller's controversial reforms have not been effective. "I don't see a lot of accomplishments," Grassley said Tuesday.

The powerful senior Republican said he spoke to acting chief of staff Mick Mulvaney but would only know if Trump heard the message if Cissna and others "don't get fired."

Sen. John Kennedy, R-La., expressed sympathy for ousted Homeland Security chief Kirstjen Nielsen, who was pressured to resign Sunday. He said she and Trump agreed to go their separate ways, and "then her colleagues on the White House staff, or at least some colleagues named 'anonymous source,' they cut her to pieces."

"They opened her up like a soft peanut," Kennedy said. "Secretary Nielsen deserved better from her colleagues, when her colleagues for whatever reason decided to gut her like a fish that was a disservice to Secretary Nielsen, to the people of America, and to the President."

He added that he thinks the backstabbing — Trump adviser Stephen Miller reportedly told Trump Nielsen was too weak for the job — "makes it doubly difficult to try and find somebody to replace her."

"Secretary Nielsen is not responsible for the wall not being built, she can't build the wall by herself. It's not Secretary Nielsen's fault that we haven't fixed the asylum laws," he said.

Sen. Susan Collins, R-Maine, noted she was involved in the creation of the DHS more than a decade ago and knows "these are vital positions."

Sen. Lindsey Graham, R.-S.C., told reporters at the Capitol that the White House should be focusing on working with Congress to fix immigration laws, and should send over the legislative changes they're looking for.

"It doesn't matter who he puts in. There's only so much they can do," Graham said.

The White House announced Monday that Secret Service Director Randolph Alles was leaving. Trump also withdrew the nomination of Ronald Vitiello to head Immigration and Customs Enforcement last week.

Acting deputy Homeland Secretary Claire Grady was in line to become acting Homeland Secretary, but offered her resignation Tuesday night, Nielsen said in a tweet. Trump had said he wanted Kevin McAleenan, who was commissioner of Customs and Border Protection, to be acting DHS head.

The Secret Service, ICE and CBP are a part of Homeland Security, and Trump is reportedly considering more changes as well.

Senate Homeland Security Committee Chair Ron Johnson, R-Wisc., told NBC News on Monday he's concerned about the "void" at DHS.

"We are dealing with a humanitarian and security crisis at the border because Congress has failed to act," Johnson said. "In addition to congressional dysfunction, I am concerned with a growing leadership void within the department tasked with addressing some of the most significant problems facing the nation."

Grassley told The Washington Post on Monday he was “very, very concerned” over the possible purge that is set to happen at DHS. But when asked about his worry on camera, Grassley was more reserved saying he was just concerned over former staffers of his who have been dismissed.

The senate's top Democrat, Chuck Schumer of New York, said Trump is to blame for the problems at the border.

The president "cannot keep changing personnel, changing strategy, tweeting your way through a problem as serious" as immigration, Schumer said.

"What he's done by these constant firings, the constant change of policy, is simply created chaos at the border. Nobody knows what the policy will be from day to day and week to week and month to month," Schumer said. "This erratic, nasty style of governing is not solving any problems."

The president on Tuesday denied that he was "cleaning house" at DHS and blamed Democrats for the immigration problems.

"I never said I'm cleaning house. I don't know who came up with that expression," Trump told reporters at the White House. "We're fighting the bad laws, the bad things coming out of Congress" and an asylum situation that's "ridiculous."