Mr. Trump's comments came as House Republicans were still preparing a vote this week on a backup immigration reform bill - but no date for the vote had been set, as GOP leaders have struggled to corral a majority on the issue.
In Congress, Mr. Trump's idea to deny due process rights to illegal aliens landed with a big thud in both parties.
"Removing due process from immigration cases is yet another example of Trump’s extreme immigration policy and disregard for the rule of law," said Rep. Frank Pallone (D-NJ).
"No person shall be…deprived of life, liberty, or property, without due process of law," tweeted Rep. Justin Amash (R-MI), quoting the text of the Fifth Amendment to the Constitution.
"Due process is a bedrock American legal principle," said Rep. Jerry Nadler (D-NY).
Democrats spent much of the weekend trying to focus more attention on the effort to reunite children of illegal immigrant families, who were separated from their parents under a Trump Administration effort to deter illegal immigrants from trying to cross the U.S. southern border.
But others on Capitol Hill saw the current immigration debate in much a different light.
"America is heading in the direction of another Harpers Ferry," said Rep. Steve King (R-IA), a strong backer of the President's calls for tough action on illegal immigration, referring to John Brown's raid in 1859, in a bid to start a slave revolt.
"After that comes Ft. Sumter," King said in a tweet, referring to the first shots of the Civil War.