"These words offend dreamers who have been brought to this country through no fault of their own, and they offend our entire nation," Rep. Ben Ray Luján (D-N.M.) said on the House floor.
House Speaker John Boehner (R-Ohio) did put some distance between himself and King, calling King's comments "wrong" and "hateful."
Rep. Rubén Hinojosa (D-Texas) said Americans expect members of Congress not to make generalizations about groups of people, and to exemplify what's good in the country.
"Recent comments made by one colleague across the aisle are far below those expectations," Hinojosa said of King.
"It is disgraceful that a member of this body would demean this House and what this country represents when you make remarks like that," added Rep. Albio Sires (D-N.J.). "When you make remarks like one of the members made, it's not only ignorant, but quite frankly stupid in not recognizing the history of this country."
"This rhetoric has no place in this institution, and it must stop," Rep. Raul Ruiz (D-Calif.) said.
Later in the day, Rep. Ted Poe (R-Texas) tweeted that he too disagrees with King's comments. "Such inflammatory and hateful comments are out of touch with reality and do nothing to fix our broken system," he said.
On Tuesday, King said his remarks were accurate and said it's accurate to say you can tell that some immigrants have been hauling drugs into the country by looking at their physique.