President Trump is spending the holidays in Florida as lawmakers are locked in an impasse over how to proceed with a Senate trial following a House vote to impeach him.

Mr. Trump traveled to his Mar-a-Lago resort in Florida on Friday evening, after signing the National Defense Authorization Act at Joint Base Andrews in Virginia. He later signed a package of government spending bills while onboard Air Force One, en route to Florida.

His trip comes after he became the third president in U.S. history to be impeached, with a historic House vote this week on two articles of impeachment: abuse of power and obstruction of Congress. The House must deliver the articles of impeachment to the Senate, which will then hold a trial overseen by Supreme Court Chief Justice John Roberts.

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Senate Majority Mitch McConnell and Minority Leader Chuck Schumer are at an impasse over the rules for the trial. Schumer has called for witnesses from the White House, including acting chief of staff Mick Mulvaney, but McConnell has indicated that's a nonstarter.

"He wants a special pre-trial guarantee of certain witnesses whom the House Democrats did not even bother to pursue themselves as they assembled their case, or he wants to proceed without any organizing resolution whatsoever," McConnell said about Schumer in a speech on the Senate floor Thursday. "So as I said, a cordial conversation, we remain at an impasse on these logistics."

House Speaker Nancy Pelosi has also said she would not send the articles of impeachment to the Senate, which adjourned until January, and that the House would not vote on impeachment managers until the Senate finalizes its plans for the trial.

Pelosi and Democrats in the House and Senate are trying to pressure the Senate to call for more documents and for witnesses who did not testify in the House impeachment proceedings because the White House prevented them from appearing.

Given that Pelosi has not transmitted the articles of impeachment to the Senate, the White House is considering making the case that Mr. Trump has not been officially impeached, two sources involved in the president's impeachment defense told CBS News this week.

The White House is considering making that case based on an opinion piece by Harvard Law Professor Noah Feldman on Bloomberg's opinion page Thursday. Feldman was one of the legal experts called by Democrats to testify before the House Judiciary Committee earlier this month and has advocated for Mr. Trump's impeachment and removal from office.

"If the House does not communicate its impeachment to the Senate, it hasn't actually impeached the president. If the articles are not transmitted, Trump could legitimately say that he wasn't truly impeached at all," Feldman wrote.

However, Harvard Law Professor Laurence Tribe wrote on Twitter that he disagreed with Feldman's analysis, saying that "under Art. I, Sec. 2, Clause 5, he was impeached on Dec 18, 2019. He will forever remain impeached. Period." That portion of the Constitution says that the House of Representatives "shall have the sole Power of Impeachment."

Two-thirds of the Senate must vote to convict Mr. Trump in order for him to be removed from office, and as the Senate is controlled by Republicans, that outcome is unlikely.

Mr. Trump slammed Pelosi on Friday, suggesting that she should be impeached. Members of Congress cannot be impeached, only voted out of office.

"Nancy Pelosi is looking for a Quid Pro Quo with the Senate. Why aren't we Impeaching her?" Mr. Trump wrote on Twitter.

The impeachment developments came in the same week that the House voted to approve the U.S.-Mexico-Canada trade agreement on a bipartisan basis, a legislative victory for Mr. Trump. The National Defense Authorization Act also establishes the Space Force, a defense priority for Mr. Trump, in a deal that Democrats agreed to in return for 12 weeks of paid parental leave for federal workers.

The president is expected to speak at the Turning Points USA Student Action Summit in West Palm Beach on Saturday evening.

—Ben Tracy contributed to this report