Washington (CNN) The first hearing in CNN and Jim Acosta's federal lawsuit against President Trump and several top White House aides ended with the judge saying that he would rule on Thursday.

CNN and Acosta are alleging that the White House's suspension of his press pass violates the First and Fifth Amendments. Their lawyers are asking for a temporary restraining order and a preliminary injunction that would restore his pass right away. They also want the administration's action deemed unconstitutional.

CNN and Acosta filed suit on Tuesday. The case was assigned to Judge Timothy J. Kelly, a Trump appointee.

On Wednesday afternoon Kelly heard arguments over the proposed temporary restraining order and preliminary injunction from Theodore Boutrous, an attorney representing CNN, and Justice Department attorney James Burnham.

The judge began by probing CNN's arguments for the better part of an hour. Then he questioned Burnham and heard rebuttals from Boutrous. The hearing lasted for nearly two hours, with Kelly scrutinizing both sides, drilling down especially deep on some of CNN's arguments.

Before dismissing court, Kelly said he would rule on the temporary restraining order Thursday at 3 p.m.

Outside the courthouse, Boutrous told reporters that the "judge was very very focused on the key issues of the case."

Boutrous said he is grateful the judge "gave us such a serious hearing" and said he is "very much looking forward to his ruling tomorrow."

Kelly opened the hearing by quizzing Boutrous on the network's First Amendment claim and asking how the President's history of attacks on CNN should be viewed in the context of the lawsuit.

Boutrous rattled off examples of Trump's missives against CNN, including his claim that the network is an "enemy of the people."

Kelly expressed skepticism that this proves the Acosta ban is "content-based discrimination," as CNN is alleging.

Kelly said there is some evidence that Acosta's conduct -- not his content -- led the White House to suspend his press pass.

But Boutrous disputed that and said there "never will there be more evidence of facial discrimination and animus against an individual reporter" than in this case.

Kelly said "we've all seen the clip" of the White House press conference where Trump and Acosta had a combative exchange last week. Kelly said that Acosta "continued speaking after his time expired" and "wouldn't give up his microphone" -- points that the Trump administration made in its briefs earlier Wednesday.

Under questioning from the judge, Boutrous cited Trump's words to Acosta from the press conference, and said, "'Rudeness' is really a code word for 'I don't like you being an aggressive reporter.'"

Kelly peppered CNN's attorney with hypotheticals as he tried to determine what a lawful move by the White House, responding to Acosta's actions, would look like.

"Could they let him keep the pass but tell him he couldn't come to presidential press conferences?" Kelly asked.

Boutrous contended that even a partial response like that would be a violation of Acosta's First Amendment rights.

Boutrous called the White House's move to revoke Acosta's hard pass "the definition of arbitrariness and capriciousness."

"What are the standards?" Boutrous asked. "Rudeness is not a standard. If it were no one could have gone to the press conference."

Boutrous separately brought up evidence that hadn't been available when CNN filed its suit: A fundraising email that the Trump campaign sent Wednesday.

The email touted the decision to revoke Acosta's credentials and attacked CNN for what it called its "liberal bias." Boutrous said that by grouping that all together in the same breath, the email made it clear that it was Acosta's coverage and not his conduct at a press conference that triggered the revocation of his press pass.

Kelly asked CNN's lawyers to state the company's position regarding the original White House accusation that Acosta placed his hands a White House intern as she tried to grab a microphone out of his hand.

"It's absolutely false," Boutrous said.

Boutrous also pointed out that Trump administration never mentioned that accusation against Acosta in the 28-page brief that Justice Department lawyers filed with the court earlier on Wednesday.

"They've abandoned that" claim, Boutrous said.

In his first question in a back and forth with the government, Kelly asked Burnham to clear up the government's shifting rationale for revoking Acosta's pass.

"Why don't you set me straight," Kelly said. "Let me know what was the reason and address this issue of whether the government's reason has changed over time."

"There doesn't need to be a reason because there's no First Amendment protection and the President has broad discretion," Burnham said.

Still, Burnham called the White House's stated reasonings "pretty consistent throughout," and walked through a series of statements that the administration has made — from Trump's first comments at the press conference to Sanders' tweets announcing the revocation to the official statement put out Tuesday after CNN filed its suit.

Burnham said Sanders' claim that Acosta had inappropriately touched a White House intern was not a part of their legal argument.

"We're not relying on that here and I don't think the White House is relying on that here," Burnham said.

Burnham said that it would be perfectly legal for the White House to revoke a journalist's credentials if it didn't agree with their reporting.

He made the assertion under questioning from Kelly, who asked him to state the administration's position in this hypothetical situation.

The judge asked if the White House could essentially tell any individual journalist, "we don't like your reporting, so we're pulling your hard pass." Burnham replied, "as a matter of law... yes."

Pressed again by the judge on Sanders' claim that Acosta had inappropriately touched the intern, Burnham said "we don't have a position" on that.

"The one consistent explanation," Burnham said, "is disorder at the press conference."

Burnham contended that revoking Acosta's hard pass was not "viewpoint discrimination" — part of a legal threshold for a First Amendment claim.

"A single journalist's attempt to monopolize a press conference is not a viewpoint and revoking a hard pass in response to that is not viewpoint discrimination," Burnham said.

Kelly tried to press for details about how Acosta's pass came to be revoked, asking Burnham who made the actual decision.

Burnham said he didn't have any information beyond what had been filed in court documents: that the revocation was first announced by Sanders on November 7 and then "ratified" by Trump the next day.

"Do you have any information to suggest that it was anyone other than Ms. Sanders that made the decision?" Kelly asked.

"No, not that I'm offering today. I'm not denying it but I don't know anything beyond what's been filed," Burnham said.

Later, Burnham argued that revoking Acosta's press pass does not infringe on his First Amendment rights because he can still call White House staffers for interviews or "catch them on their way out" of the building.

"I think the harm to the network is very small," Burnham said.

"Their cameras are still in there," he added.

Burnham said CNN had made an "odd First Amendment injury" claim and suggested that Acosta could do his job "just as effectively" watching the President's appearances piped into a studio on CNN.

"The President never has to speak to Mr. Acosta again," Burnham said. "The President never has to give an interview to Mr. Acosta. And the President never has to call on Mr. Acosta at a press conference."

"To be in a room where he has no right to speak... this seems to me like an odd First Amendment injury that we're talking about," Burnham said.

Boutrous, the CNN attorney, fired back on rebuttal.

"That's not how reporters break stories. It's simply a fundamental misconception of journalism," Boutrous said, adding how unscheduled gaggles and source meetings throughout the White House amounted to "invaluable access."

In a legal filing by the Justice Department on Wednesday, the White House asserted that it has "broad discretion" to pick and choose which journalists are given a permanent pass to cover it.

That position is a sharp break with decades of tradition. Historically both Republican and Democratic administrations have had a permissive approach to press access, providing credentials both to big news organizations like CNN and obscure and fringe outlets.

Acosta's suspension -— which took effect one week ago — is an unprecedented step. Journalism advocates say it could have a chilling effect on news coverage.

CNN and Acosta's lawsuit was filed on Tuesday morning, nearly one week after Acosta was banned.

Before the hearing began, CNN's lawyers said the case hinges on Acosta and CNN's First Amendment rights; the shifting rationales behind the ban; and the administration's failure to follow the federal regulations that pertain to press passes, an alleged violation of Fifth Amendment rights. The lawsuit asserts that this ban is really about Trump's dislike of Acosta.

The "reasonable inference from defendants' conduct is that they have revoked Acosta's credentials as a form of content- and viewpoint-based discrimination and in retaliation for plaintiffs' exercise of protected First Amendment activity," CNN's lawsuit alleges.

In addition to the temporary restraining order and preliminary injunction that CNN is seeking at the hearing, CNN and Acosta are also seeking what's known as "permanent relief." The lawsuit asks the judge to determine that Trump's action was "unconstitutional, in violation of the First Amendment and the Due Process Clause of the Fifth Amendment." This could protect other reporters against similar actions in the future.

"If the press is not free to cover the news because its reporter is unjustly denied access, it is not free," former White House correspondent Sam Donaldson said in a declaration supporting CNN that was filed with the court on Tuesday. "And if denying access to a reporter an organization has chosen to represent it -- in effect asserting the president's right to take that choice away from a news organization and make it himself -- is permitted, then the press is not free."

Ted Olson, a Republican heavyweight who successfully argued for George W. Bush in Bush v. Gore, is representing CNN, along with Boutrous — himself another prominent attorney — and the network's chief counsel, David Vigilante.

Olson said Tuesday that while it was Acosta whose press pass was suspended this time, "this could happen to any journalist by any politician."

He spoke forcefully against Trump's action. "The White House cannot get away with this," Olson said.