In the meeting, Trump criticized the tentative bipartisan agreement drafted by Durbin, Arizona Republican Jeff Flake and four other senators.
Trump blasted the proposal as "a big step backwards" and said it didn't provide enough funding for a wall along the U.S.-Mexico border, a key campaign promise Trump made in 2016.
Earlier in the week, Trump had assured lawmakers that he would accept any agreement crafted by Congress.
"I will be signing," he said in a Cabinet Room meeting Tuesday. "I'm not going to say, 'Oh, gee, I want this or that.' I'll be signing it."
In the wake of Trump's comments, attention has shifted away from the contents of a proposed DACA deal to a statement many view as racist.
"President Trump's comments are racist and a disgrace," said Maryland Rep. Steny Hoyer, the second-ranking Democrat in the House. "They do not reflect our nation's values."
Democratic Rep. Cedric Richmond of Louisiana, who chairs the Congressional Black Caucus, said the latest statement is "yet another confirmation of [Trump's] racially insensitive and ignorant views."
He added, "[The] president's slogan 'Make America Great Again' is really code for 'Make America White Again.' "
Some Republicans also criticized Trump.
Utah Republican Rep. Mia Love, whose family descended from Haiti, called the president's comments "unkind, divisive [and] elitist."
They "fly in the face of our nation's values," Love added. "This behavior is unacceptable from the leader of our nation."
Sen. Susan Collins of Maine told Patty Wight of Maine Public Radio that the president should not denigrate citizens of other countries and that "it does not help us come up with a bipartisan approach to immigration."
But Republican leaders like House Speaker Paul Ryan largely remained silent on the matter, although on Friday morning Ryan described Trump's comments as "very unfortunate, unhelpful."
Other GOP lawmakers struck the now-familiar balance of distancing themselves from the president's statements, but not criticizing Trump himself. Arizona Rep. Paul Gosar told NPR's Morning Edition that he "can't condone vocabulary that another person actually utilizes in that aspect." But, he added, "I also understand the president is not a career politician, and may say things that are politically incorrect."
"Any word can be utilized in an offensive aspect," Gosar said.
Editor's note: NPR has decided in this case to spell out the vulgar word that the president reportedly used because it meets our standard for use of offensive language. It is "absolutely integral to the meaning and spirit of the story being told."