Trump admin live updates: Trump strikes deals with law firms totaling $600M

The House’s feud over proxy voting for new parents that paralyzed the chamber is on the back burner after Republicans voted to effectively kill GOP Rep. Anna Paulina Luna’s measure and formalize “vote-pairing.”

Republicans passed a rule -- a procedure to advance legislation -- Tuesday afternoon by a vote of 213-211 that included language to formalize vote-pairing and make Luna’s original measure moot.

Speaker Mike Johnson and Luna cut a deal over the weekend to formalize vote pairing, which is a procedure that allows a member who is absent during a vote to coordinate with a present member on the other side of the matter to offset the absence. It’s certainly not an equivalent to remote voting but allows for an absence to be offset.

Luna's bipartisan discharge petition would have allowed proxy voting for new parent lawmakers -- both mothers and fathers -- up to 12 weeks after giving birth.

But House Democratic Caucus Chairman Pete Aguilar said Democrats “won’t participate” in vote-pairing.

“This is a fake and phony effort … we won’t be engaging in this pairing effort,” he said at a news conference Tuesday at the Capitol.

-ABC News’ Lauren Peller

Trump-appointed Judge Trevor McFadden granted a preliminary injunction ordering the White House to restore access to The Associated Press in the Oval Office, on Air Force One and other spaces open only to the press pool.

"[W]hile the AP does not have a constitutional right to enter the Oval Office, it does have a right to not be excluded because of its viewpoint," McFadden wrote.

"Indeed, the Government has been brazen about this," McFadden added, pointing to the president's objection to the AP's continued use of the "Gulf of Mexico" rather than Trump's preferred "Gulf of America."

"The Government offers no other plausible explanation for its treatment of the AP. The Constitution forbids viewpoint discrimination, even in a nonpublic forum like the Oval Office."

Throughout his 41-page ruling, the judge relied heavily on the testimony of AP photographer Evan Vucci and correspondent Zeke Miller, both of whom told the court last month that their inability to serve alongside their pool colleagues set the AP's journalism back, causing "damaging ripples across its reporting capabilities."

"These disadvantages have poisoned the AP's business model," McFadden said.

The judge noted that since the AP filed its suit, the White House has set aside the traditional role of the White House Correspondents' Association and taken it upon itself to determine how the pool is constituted.

Nevertheless, McFadden wrote, it is unconstitutional for the president to single out and ban a disfavored outlet because of its viewpoint.

McFadden stayed his own order until Sunday "to provide the Government time to seek an emergency stay from a higher court and to prepare to implement the Court's injunction."

-ABC News' Steven Portnoy

The press secretary was asked about President Donald Trump's suggestion that American criminals could be deported to El Salvador prisons.

Leavitt responded that it's an "idea that he has simply floated and discussed," but claimed that the legality of such a move is questionable.

"These would be heinous, violent criminals who have broken our nation's laws repeatedly. And these are violent repeat offenders in American streets. The president has said if it's legal, right, if there is a legal pathway to do that, He's not sure. We are not sure if there is," she said.

White House press secretary Karoline Leavitt said Tuesday that next Monday, on April 14, Trump will welcome El Salvador's President Nayib Bukele.

"They will discuss El Salvador's partnership on using their supermax prison for Tren de Aragua and MS-13 gang members, and how El Salvador's cooperation with the United States has become a model for others to work with this administration," Leavitt said.

The administration's deportations of alleged gang members to El Salvador's faced numerous legal challenges, including a case where a Maryland man was removed to the Central American nation by mistake.