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Outside the House chamber, Rep. Ryan Costello, R-Pa., said Trump's tweet - which may simply reflect a recognition that the conservative bill was doomed anyway - could sway undecided Republicans to vote against the more moderate bill.

MCALLEN, Texas (AP) - Demonstrators led rallies and protests on Saturday to decry the separation of immigrant parents from their children by United States border authorities, while Democratic lawmakers said they aren't convinced the Trump administration has any real plan to reunite them.

Republican Rep. Mike Simpson of Idaho said lawmakers who are counting on Trump to provide a presidential nudge should reconsider. He said one of the barriers he found then for Congresspeople looking to pass reform is the fear of losing their seat in an upcoming election, which is why he said he does not expect to see anything coming out of the House this week.

GOP leaders said they'd press on anyway, but his comments further damaged their attempt to win over wavering lawmakers for a measure already facing likely defeat.

Despite his concession on Wednesday, Trump suggested yesterday that some of the wrenching tales that have emerged from the border were fabricated by Democrats, tweeting, "We can not allow our Country to be overrun by illegal immigrants as the Democrats tell their phony stories of sadness and grief, hoping it will help them in the elections".

Lawyers working to bring families back together said they were struggling through a labyrinthine process - while more migrants continue to arrive.

Republican leaders were trying to persuade colleagues to seize the moment and tackle immigration problems by approving the bill, which includes 25 billion dollars for Mr Trump's border wall and a path to citizenship for young immigrants who have lived in the U.S. illegally since childhood.

There were some 2,053 of those children as of Wednesday, when President Trump signed his executive order ending family separation at the border.

After images of children in chain-link enclosures sparked domestic and global outrage, the president ended the separation practice but has continued his hardline talk on immigration.

A pile of kids shoes left by mayors from USA cities lay at the front gate outside of the children's tent encampment built to deal with the Trump administrations "zero tolerance" policy in Tornillo, Texas.

The public defender for the western district of Texas said they would not.

Last week, Trump reversed a policy of separating families entering the USA illegally at the border with Mexico.

The House bill still under consideration is a compromise between conservatives and moderate Republicans.

If a bill makes it through the House, it would still have to be supported by several Senate Democrats to pass both houses. "Most children come without parents".

The Trump administration announced plans in April to prosecute all immigrants caught along the southwest border with illegally entering the country.

President Donald Trump earlier in the day blamed Democrats for the ongoing impasse. "If the president said to a given bill, "That's my bill; that's the one I want" - I think that would have a pretty significant impact on our discussions".

Donald Trump is taking a step back from his immigration push.

The legislation has taken on new urgency as the executive order appears to be temporary and is expected to face legal challenges in connection with the Flores agreement, a landmark 21-year-old court settlement under which immigrant minors can be detained no longer than 20 days.