Louisiana Republican Rep. Steve Scalise, the leader tasked with rounding up votes, told reporters: "I want to see us pass this bill and let the Senate have the opportunity to take it up as well and solve the problem".
"Ms Grisham went on to say that "[Melania] believes we need to be a country that follows all laws, but also a country that governs with heart", a line which supports the president's recent policy decision to criminally prosecute all adults attempting to cross illegally into the U.S. over the southern border. The Trump administration is now fighting a lawsuit brought by the American Civil Liberties Union that would require families to be reunited after they are separated during criminal proceedings. The result has been almost 2,000 minors separated from their families because children can not be jailed with their parents.
The Republican-controlled House of Representatives is expected to consider two immigration bills.
The President early indicated he does not want to support either of two bills created to move towards a solution to the family separation issue.
"While cases are pending, families should stay together", tweeted Senator Cruz, who is in an unexpectedly tough re-election battle. He introduced his own bill to speed up court proceedings to no more than 14 days.
Unaccompanied minors are also an issue for this administration, with the government confessing it had lost 1500 children placed in homes or foster families, prompting the viral hashtag #wherearethechildren?
The ACLU's petition asking that Homeland Security end the "vicious and inhumane" practice of separating children from their parents now has upward of 150k signatures, and is seeking at least 50k more. "Now", said Rep. Fred Upton of MI, adding: "It's never acceptable to use kids as bargaining chips in political process." Sen. Kansas GOP Sen. Pat Roberts said he is "against using parental separation as a deterrent to illegal immigration".
"The time is now for the White House to end the cruel, tragic separations of families", said Senator Lisa Murkowski, from Alaska.
In some cases, parents are deported before finding their children in ORR custody, said Lisa Frydman, a KIND attorney. John McCain tweeted that the policy is an "affront to the decency of the American people, and contrary to principles and values upon which our nation was founded". "It should do so now".
"The United States will not be a migrant camp and it will not be a refugee holding facility", Trump said.
Homeland Security Secretary Kirstjen Nielsen said in an appearance before the National Sheriffs' Association in New Orleans: "We will not apologise for the job we do or for the job law enforcement does, for doing the job that the American people expect us to do. We need the wall" and spoke at length about the need for funding.
Leaders in both the House and Senate are struggling to shield the party's politicians from the public outcry over images of children taken from migrant parents and held in cages at the border.
It was unclear if any progress was made, but White House spokesman Raj Shah said in a statement that Mr Trump told the group of lawmakers he would endorse their immigration legislation. The president said his administration wants safety and security for the country.
The bill also says that illegal immigrant parents charged with misdemeanors, who normally would be sent to the criminal justice system's jails, can be held in immigration detention - meaning they can remain with their children. McClatchy obtained draft bill text Tuesday afternoon.
Trump spent 45 minutes ranting to House Republicans on everything from taxes to his pending lawsuits Tuesday evening, according to members in the meeting, while offering barely any info about whether he'd support the specifics of a pair of bills that closely follow the President's own policy goals on immigration. He said the U.S. has the worst immigration laws in the world. The law wasn't being enforced beforehand.
Hearing silence from the room, Trump then piled on and said, "What, nobody gets it", and added that Sanford is a "nasty guy".
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