Washington (CNN) Congressional Republicans, keen to secure an end to a policy separating children from their parents at the US border, received unclear marching orders from President Donald Trump on Tuesday after a meeting on Capitol Hill.

Some lawmakers emerged from the hour-long huddle adamant Trump had endorsed a compromise measure that would allow families to remain together.

But others were more equivocal, saying Trump only expressed support for any bill that arrives on his desk -- either the compromise plan or a more conservative version whose prospects appear dim.

The White House said afterward Trump "endorsed both House immigration bills," which also provide funding for his promised border wall and close certain immigration loopholes.

But the lack of a clear endorsement for either plan quieted GOP hopes for presidential momentum.

"It's always nice to see the President but this didn't move the ball," one Republican lawmaker said.

The meeting came at a pivotal moment -- both for Trump's presidency and his party -- as the GOP-controlled House of Representatives prepares to hold major votes on two very different immigration bills this week. It also happened following images and audio of children being detained in cages flashed across television sets, leading to widespread uproar.

Trump acknowledged during the session the images look bad, multiple lawmakers said afterward. But he did not indicate he was preparing to take any steps to end the family separation practice.

Departing Capitol Hill, Trump said briefly he had a "great meeting" with his fellow Republicans.

"These are laws that have been broken for many years, decades," Trump said. "But we had a great meeting."

'A total miscue from the administration'

Ahead of his meeting on Tuesday evening, Trump went back and forth about whether he would support one of the bills set to come to the floor this week, even though his own White House helped negotiate that very measure.

The White House has indicated, and again indicated after the meeting, Trump backed both immigration bills pending in the House: One meant to appeal to conservative members, and another more moderate compromise.

Emerging from the conference meeting, some Republicans said Trump was clear he would approve the compromise bill if it passes.

Rep. Chris Collins, a New York Republican, said the President was "crystal clear" during the meeting that he is behind the compromise legislation.

Other GOP lawmakers, including Rep. Mia Love of Utah and Rep. Ted Yoho of Florida, also said they took Trump's remarks as an endorsement of the measure.

But other Republican lawmakers indicated Trump did not specifically voice support for the compromise bill.

The White House said he still backs both.

"He told the members, 'I'm with you 100%,'" said Raj Shah, a White House spokesman.

Before the meeting, some Republicans were skittish that the President could thwart the hard-fought compromise bill with a random tweet or off-the-cuff comment. After it, lawmakers across the GOP spectrum expressed frustration that Trump hadn't lent his explicit support to either plan.

A GOP leadership source said the meeting was not helpful for the prospects of passing either bill. And a source in the conservative Freedom Caucus source was even harsher: "It's a total miscue from the administration. Both of these bills are designed to fail, and the President is the only one who doesn't get the joke."

Just hours before heading to the Hill Tuesday, Trump unloaded on Democrats over immigration, once again blaming them for the family separations and accusing them on Twitter of wanting "illegal immigrants, no matter how bad they may be, to pour into and infest our Country, like MS-13."

And in a speech, he strayed from his prepared remarks to express frustration about the issue and said he planned to make changes to the legislation.

"So, we have a House that's getting ready to finalize an immigration package that they're going to brief me on later, and then I'm gonna make changes to it," Trump said while speaking to small business owners in Washington. "We have one chance to get it right. We might as well get it right, or let's just keep it going."

What Republicans have been working on

Republicans have been working behind closed doors for weeks to hammer out an agreement that will make it possible for members on both ends of the GOP spectrum to get a vote on an immigration bill they prefer.

One bill, known as the Goodlatte bill -- after its direction from Republican Rep. Bob Goodlatte of Virginia -- appeals to the more conservative hardline wing of the party.

The other legislation, known as the compromise bill, aims to give recipients of the Deferred Action for Childhood Arrivals program , an eventual path to citizenship while also giving the President and his supporters $25 billion for border security and his signature wall.

In the uproar over family separations, Republicans have also been crafting what they see as a legislative approach that would keep families together in detention, a provision that they've added to both bills.

Trump's comments about making "changes" were referencing the new provision on family separation, multiple sources told CNN.

Lawmakers in both the House and the Senate have also been introducing their own standalone proposals on family separation in case the two immigration bills fail. Rep. Mark Meadows, chairman of the conservative House Freedom Caucus, has a measure that would keep families together in while in custody of the Department of Homeland Security.

On the Senate side, Republican Sen. Ted Cruz of Texas is proposing to speed up the asylum process, double the number of immigration judges and mandate families must be kept together. Sen. John Cornyn, the No. 2 Republican in the Senate, is re-introducing his 2014 proposal designed to keep families together, but speed up court dates and the deportation process for minors.

Public outrage growing, Congress called to act

Saddling the debate is mounting public outrage from both sides of the aisle over families being ripped apart at the border. Last month the Trump administration started prosecuting all immigrants who attempt to illegally cross the border, resulting in children being separated from their parents who undergo criminal prosecution.

According to a new CNN poll, two-thirds of Americans disapprove of the practice, while only 28% approve. A majority of Republicans, however, support the policy, demonstrating why GOP lawmakers face a political puzzle in resolving the issue. Many don't want to see families separated but they also don't want to return to the previous "catch and release" policy. That entailed detaining families, then letting them go into the United States while serving them with a court date.

"I don't think the answer to family separation is to not enforce the law," said Senate Majority Whip John Cornyn. "I think the answer to family separation is to not separate families while you are enforcing the law."

Republican Rep. Jeff Denham of California, one of the lead negotiators on the compromise bill, said on CNN that "there is only a limited amount of options you can have at the border."

"You can let them run freely and keep the family together, or you can have quick due process at the border -- adjudicating the issue immediately so that you don't have a long detention time in one of these centers," he continued. "But you got to keep the family together."

Even if the provision passes, Democrats say it's not enough to let the families stay together in detention. Rather, they're calling for Trump to simply reverse the new policy to prosecute all immigrants making illegal crossings.

"So you put them in a correctional facility with their parents? Hooray, isn't that nice. You put them behind bars? Isn't that wonderful. What a compassionate alternative that is," House Minority Whip Steny Hoyer told reporters on Tuesday. "No, we don't think that's an alternative."

This story has been updated with additional developments.