Senate Republicans Tuesday voted for a measure declaring the impeachment proceedings against former President Donald Trump to be unconstitutional because Trump is no longer in office.

The motion, from Sen. Rand Paul, R-Ky., was defeated by a vote of 55-45, showing Democrats have an uphill climb of securing the 67 votes needed for a conviction. Among those who voted for Paul’s motion was Senate Minority Leader Mitch McConnell, who’s said he’s undecided on whether to convict Trump and who worked on the trial calendar with Senate Majority Leader Chuck Schumer.

McConnell, when he was still majority leader, rebuffed Democrats’ efforts to hold the trial while Trump was still in office.

Senators were sworn for Trump’s second impeachment trial earlier Tuesday, a day after House impeachment managers delivered to the Senate the article of impeachment against Trump for incitement of insurrection in the Capitol riot earlier this month.

The senators were given the oath by Sen. Patrick Leahy, D-Vt., the president pro tempore of the Democratic-controlled Senate.

“Do you solemnly swear, that in all things appertaining to the trial of Donald John Trump, former president of the United States, now pending, you will do impartial justice according to the Constitution and the laws, so help you God?” Leahy asked the assembled senators.

Leahy is presiding over the trial instead of Chief Justice John Roberts because Trump is now a former president.

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Trump’s “former” status has led several Republicans to argue that he can’t be subjected to an impeachment trial, because the Constitution says “judgment in cases of impeachment shall not extend further than to removal from office, and disqualification to hold and enjoy any office of honor, trust or profit under the United States.”

One proponent of that view, George Washington University law professor Jonathan Turley, spoke to Senate Republicans at a lunch ahead of the swearing-in on Tuesday. Turley, who testified against Trump’s first impeachment in the House, has said he is against the second impeachment as well, calling it “at odds with the language of the Constitution” because the trial is taking place with Trump no longer in office.

“They have a tough decision to make,” Turley told reporters after the lunch.

Paul, meanwhile, pushed for a vote on the constitutionality issue on the Senate floor Tuesday. “Private citizens don’t get impeached. Impeachment is for removal from office, and the accused here has already left office,” he said.

“This impeachment is nothing more than a partisan exercise designed to further divide the country,” Paul added. “Democrats claim to want to unify the country, but impeaching a former president, a private citizen, is the antithesis of unity.”

Paul celebrated the strong support from his fellow Republicans. “45 Senators agreed that this sham of a ‘trial’ is unconstitutional. That is more than will be needed to acquit and to eventually end this partisan impeachment process. This ‘trial’ is dead on arrival in the Senate,” he tweeted after the vote.

But Sen. Rob Portman, R-Ohio, later claimed his vote only meant he was in favor of debating the constitutionality issue, and that the vote doesn’t necessarily mean he won’t vote to convict at the end of the trial. “It’s a totally different issue as far as I’m concerned,” Portman said.

Only five of 50 Republican senators voted in favor of “tabling” – essentially killing – Paul’s motion. They were Ben Sasse of Nebraska, Susan Collins of Maine, Mitt Romney of Utah, Lisa Murkowski of Alaska and Pat Toomey of Pennsylvania.

“In my view, the text and context of the Constitution, the meaning of the term ‘impeachment’ to the founders, and the most relevant precedents indicate that it is constitutionally permissible for the Senate to consider the impeachment of President Trump,” Toomey said in a statement afterwards.

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Democrats maintain they have precedent on their side. While no former president has been tried by the Senate after leaving office, Secretary of War William Belknap was tried in the Senate in 1876 after he had already resigned.

And legal experts, such as Harvard law professor Laurence Tribe and University of Texas law professor Steve Vladeck, stress that the trial is constitutional because one of the considerations the Senate must make is whether to bar the subject of impeachment from future office.

Democrats note that Trump was impeached by the House while he was still in office, and maintain a trial is necessary to hold him accountable for what Schumer, D-N.Y., called “the most despicable thing any president has ever done,” inciting a riot at the Capitol while a joint session of Congress was counting the Electoral College vote.

If Trump were to be convicted by a two-thirds vote, the Senate could then vote to disqualify him from holding office in the future.

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“The only thing that I need to know is that, in the midst of an assault on our Capitol, where thousands of armed and angry rioting supporters of President Trump were beating Capitol Police officers in one case bludgeoning a Capitol Police officer to death, and breaking into the Capitol, and threatening the Congress, and trying to stop the certification of an electoral vote, at that moment, President Trump was gleeful and declined requests to dispatch the National Guard, and took no action to restrain his supporters, and made no effort to check on the safety of his own vice president or the leaders of Congress,” Sen. Chris Coons, D-Del., told MSNBC’s “Morning Joe” on Tuesday. “That alone to me is evidence enough to convict on the charge that was presented to the Senate yesterday,”

“To me, there has to be accountability, and (impeachment) is the accountability tool the Constitution gives us,” Coons said.

In an interview with Hugh Hewitt Tuesday morning, Sen. Ted Cruz, R-Texas, straddled the differences of opinion, saying, “I actually think the question of whether an ex-president can be impeached is a close question. I think there are strong and serious Constitutional arguments on both sides of the question.”

But, Cruz added, “I think this impeachment is a mistake. I think it is petty and vindictive on the Democrats’ part, and I think they’re engaged in political retribution. And so I’m going to vote against conviction.”

In the afternoon, Cruz voted in favor of Paul’s motion that the trial is unconstitutional.

While some senators have likened their role in the impeachment trial to jurors, they’re actually more than that. They can vote to overrule Leahy and make decisions about the admissibility of evidence and witnesses.

Then-Chief Justice William Rehnquist, when he was presiding over the impeachment trial of Bill Clinton in 1999, noted, “The Senate is not simply a jury. It is a court in this case.”

In this particular trial, they are victims as well, after having to scramble for safety after a mob of Trump supporters stormed the Capitol on Jan. 6. Five people were killed in the mayhem, including a Capitol Police officer, Brian Sicknick.

The Senate trial is expected to begin the week of Feb. 8 under a deal struck between the parties. Senate Republicans had requested extra time to allow Trump’s lawyers to prepare.

The Democratic-controlled House approved the article of impeachment on Jan. 13 in a 232-197 vote; 10 Republicans sided against Trump, the most bipartisan vote on a presidential impeachment in history, doubling the five Democrats who voted to impeach Clinton.