In the Senate, Republican Senator Ted Cruz, who ran unsuccessfully against Trump in 2016 for their party's presidential nomination, said he would introduce legislation this week to halt family separations.
May said Wednesday that images of children in cages were "deeply disturbing".
But a defiant Trump sounded unfazed by the mounting pressure to alleviate the situation before it ruptures into a public relations disaster for his party.
Reps. Chris Collins (R-N.Y.) and Carlos Curbelo (R-Fla.) said Trump told Republicans that his daughter Ivanka had approached him concerned about the images of family separation.
He used the word "infest" to describe migrants coming to the USA illegally.
After his remarks, the president raised eyebrows by walking across the stage, arms outstretched, and embracing a United States flag.
On Wednesday, he claimed the Democrats "won't give us the votes to pass good immigration legislation". They want open borders, which breeds disgusting crime.
The House is set to vote later in the week on two immigration bills, including provisions that would curb the separation of children from their parents at the border.
One is a hardline measure favored by conservatives, and is unlikely to pass.
Senate Judiciary Committee Chairman Chuck Grassley said he's pushing a bill that would repeal the Flores settlement, which would allow the families to be detained longer than 20 days together in immigration detention.
But Trump himself put that bill in doubt.
White House aides have refused to comment on rumors of an executive order prior to Trump's unscheduled remarks to reporters, and Republicans on Capitol Hill seemingly have no knowledge of a coming executive action.
Meanwhile, Democrats spent the morning calling on Trump and congressional Republicans to end the policy in speeches on the House floor. "Congress should act quickly on a legislative solution to fix this problem", Portman tweets, and yet he is still one of the exclusively Republican list of 51 senators that have not signed on board with Keep Families Together Act.
It's unclear exactly what the president might be supporting, but he said he would be signing something "in a little while".
The reversal by Trump comes weeks into his administration's new policy to criminally prosecute all migrants who are caught crossing the border illegally; in such prosecutions, adults are separated from any children traveling with them. "Yes, I love children a great deal, but to me, it's up to the parents to do things rightfully and legally".
"Like I said earlier, it's the parents that bring them up, and they already know they're going to take them away, so to me there's no issue there", Carroll said. Ted Cruz and John Cornyn who have already announced they're writing a counterpiece of legislation Is it that hard for Republicans to get behind a Democrat-introduced piece of legislature, or are they really willing to let children sleep in cages where babies have their diapers changed by other children so Republicans can take their sweet time throwing together their own version of legislation?
Babies and toddlers have been sent to three "tender age" shelters maintained by the Department of Health and Human Services, the Associated Press news agency reports.
Most crossed the border without their parents.
McMorris Rodgers said in a statement Monday that "the administration should stop the practice of separating families on their own". A CNN-SSRS poll revealed that even among those who approve of the job Trump is doing as President, a quarter disapprove of the policy.
But activists seized on the symbolism.
As the administration faces growing outrage over its "zero tolerance" crackdown, Trump officials say they are committed to helping parents locate their children and avoid being deported without them.
Mr Trump has declared the USA "will not be a migrant camp" on his watch, saying on Monday: "I say it's very strongly the Democrats' fault".