WASHINGTON — The clock wound down on Thursday as senators posed questions to impeachment trial lawyers in an effort to consider whether to remove President Trump from office.

Senators are expected to vote Friday on whether to hear new witnesses, and Republicans gained ground late Thursday night after Senator Lamar Alexander of Tennessee, a critical swing vote, said he would vote against considering any new evidence before deciding whether to remove President Trump from office.

The first part of Thursday’s session focused largely on the arguments of one of Mr. Trump’s lawyers, Alan M. Dershowitz, who said the president has very broad powers to do what he must in order to be re-elected.

Here are some of the takeaways so far.

Senator Lamar Alexander said late Thursday that he would vote against considering additional witnesses, a strong indication that Republicans have lined up the votes to block a call for more documents and witnesses.

Mr. Alexander did not contest the charges that Mr. Trump withheld military aid from Ukraine in order to get the country to investigate his political rival, and said he considered that conduct “inappropriate.” But he added that it was not impeachable.

Democrats would need four Republicans to join them in voting for a motion to consider additional witnesses and documentary requests. But so far, only two Republican senators, Susan Collins of Maine and Mitt Romney of Utah, have indicated they will do so.

A fourth possible Republican swing vote, Senator Lisa Murkowski of Alaska, has yet to announce her decision. Both parties deemed it nearly impossible that any other Republican senator would defect.

Ms. Murkowski seemed to hint at her state of mind with a question directed to the president’s lawyers: “Why should this body not call Ambassador Bolton?”

Mr. Alexander’s opposition, announced after the conclusion of a second marathon day of questioning by senators, was a significant victory for Republican leaders the day before a crucial vote on Friday that will determine whether the trial moves toward a swift conclusion or a prolonged quest for more information.

In one of the most closely watched moments, Senator Rand Paul, Republican of Kentucky, tried to force the chief justice to read a question aloud that included the name of a person widely thought to be the C.I.A. whistle-blower whose complaint prompted the impeachment inquiry.

“The presiding officer declines to read the question as submitted,” the chief justice, John G. Roberts Jr., said after silently reading the question card.

Over the course of the Ukraine affair, Mr. Trump has called for the whistle-blower to come forward, at times suggesting that the intelligence officer was acting as a spy. Government officials normally make every possible effort to protect a whistle-blower‘s identity.

When the chief justice declined to read his question, Mr. Paul left the Senate chamber and held a news conference in a nearby room where he read aloud the question himself and later posted it on social media. It “deserved to be asked,” said Mr. Paul, who has repeatedly called on media organizations to reveal the whistle-blower’s name.

Mr. Paul’s question did not mention the term “whistle-blower,” and the senator later said that he had no independent knowledge of the whistle-blower’s identity. Three names were included in the question, which addressed whether any officials on the National Security Council also worked there during the Obama administration and conspired with staff members who work for Representative Adam B. Schiff, the lead impeachment manager, to plot Mr. Trump’s impeachment.

Mitch McConnell, the Senate majority leader, called for his colleagues to respect the chief justice’s position, a request that appeared to have been directed at Mr. Paul.

Democrats have questioned a broad argument made by Alan M. Dershowitz on Wednesday, that anything a president does to help himself get re-elected is inherently in the public’s interest, including a “quid pro quo.” Mr. Dershowitz said Thursday on Twitter that his remarks had been mischaracterized.

“What we have seen over the last couple days is a descent into constitutional madness,” Mr. Schiff said, responding to a question from Senator Jon Tester, Democrat of Montana.

Mr. Dershowitz’s argument drew attention on Wednesday when he said, “If the president does something that he thinks will help him get elected, in the public interest, that cannot be the kind of quid pro quo that results in impeachment.”

Mr. Dershowitz was responding to what appeared intended to be a softball question posed by Senator Ted Cruz, Republican of Texas, who has disparaged the impeachment case and started a podcast called “Verdict with Ted Cruz.”

Democrats and many constitutional scholars have attacked Mr. Dershowitz’s claim, and Mr. Dershowitz on Thursday said his words had been misconstrued.

On Thursday, Mr. Schiff said that the argument from Mr. Trump’s defense team “compounded the dangerous arguments that they made that no quid pro quo is too corrupt if it helps your election campaign by saying, and if what you want is targeting your rival, it’s even more legitimate.”

The Democratic senators Sherrod Brown, of Ohio, and Ron Wyden, of Oregon, went after the Trump legal team’s assertion that it was acceptable for the president to seek from a foreign government derogatory information on a political opponent to improve his chances in the 2020 election.

The senators used previous comments from Mr. Trump’s handpicked F.B.I. director to disprove the Trump team’s theory.

“That is something the F.B.I. would want to know about,” the agency’s director, Christopher Wray, told senators in May when speaking about offers of foreign election assistance.

American intelligence agencies concluded that Russia interfered in the 2016 presidential election.

Mr. Trump, at the time, responded that Mr. Wray was wrong. And weeks later, Mr. Trump said “I’d take it” if Russia offered him damaging information on a rival candidate.

The president’s defense team on Wednesday made the point again. “Mere information is not something that would violate the campaign finance laws,” said Patrick Philbin, one of Mr. Trump’s lawyers.

On Thursday, Democrats pushed back on that view emphatically.

“It would send a terrible message to autocrats and dictators and enemies of the democracy and the free world,” said one of the House managers, Representative Hakeem Jeffries, Democrat of New York. “For the president and his team to essentially put out there for all to consume that it is acceptable in the United States to solicit foreign interference in our free elections or accept political dirt — simply to try to cheat in the next election.”

The Federal Election Commission is on the side of Mr. Wray and the House managers.

“Anyone who solicits or accepts foreign assistance risks being on the wrong end of a federal investigation,” the commission’s chair, Ellen Weintraub, wrote in a memo last summer, adding that any such offer should be reported to the F.B.I.

Senator Susan Collins of Maine and three other Republican senators raised a key question about whether there is an appropriate way for a president to “request a foreign country to investigate a U.S. citizen, including a political rival, who is not under investigation by the U.S. government.”

Both the House managers and the Trump team responded that there were indeed legitimate ways to do this in certain circumstances, but that was just about all they agreed on.

Mr. Schiff, on behalf of the House managers, answered, “It would be hard for me to contemplate circumstances where that would be appropriate.” He said that one of the most important outcomes of Watergate was that protections were put in place to prevent politically motivated investigations.

He said that there is a formal process for the Justice Department to make such a request, and that would be under the mutual legal assistance treaty.

“There is a legitimate way to do that,” Mr. Schiff said. “That didn’t happen here.”

Mr. Philbin said that Mr. Trump never asked Ukraine for an investigation.

What he did ask, Mr. Philbin said, was if Mr. Zelensky “‘can look into it.'” The lawyer said that does not amount to Mr. Trump asking Mr. Zelensky to investigate former Vice President Joseph R. Biden Jr. and his son, Hunter Biden.

Mr. Philbin, who previously worked at the Justice Department, argued that if an American in a foreign country did something that might have been against the local law, though not against United States law, and that there was a “national interest” for the United States to know what had occurred, “then it would be perfectly legitimate to suggest this is something worth looking into.”

Not only did that answer differ from Mr. Schiff’s, it also contradicted what another member of Mr. Trump’s defense team, Robert Ray, said earlier.

“Many of you may come to conclude, or may have already concluded, that the call was less than perfect,” Mr. Ray said on Monday. “It would have been better in attempting to spur action by a foreign government in coordinating law enforcement with our government to have done so through proper channels.”

However, Mr. Ray said, what happened on the call is not an impeachable offense.

Senator Elizabeth Warren of Massachusetts, a Democratic presidential candidate, asked a question that elicited a rare reaction from the chief justice in the chamber on Thursday.

Directed to the House managers and, because of the Senate rules, read aloud by Chief Justice Roberts, Ms. Warren asked, “Does the fact that the chief justice is presiding over an impeachment trial in which Republican senators have thus far refused to allow witnesses or evidence contribute to the loss of legitimacy of the chief justice, the Supreme Court and the Constitution?”

Some senators and others in the chamber gasped, but the chief justice showed little emotion though he did let slip a small grimace.

Mr. Schiff drew the short straw and answered the question on behalf of the House managers.

“I would not say that it contributes to a loss of confidence in the chief justice,” Mr. Schiff said.

The chief justice’s limited role in the bitterly partisan Senate trial was always going to be an challenging one that could put his reputation for being objective at risk. He is presiding over a historic trial in a makeshift courtroom without the familiar norms of the justice system, and where his duties are more referee than judge.

Mr. Schiff used the opportunity to once again argue that the trial should allow new witnesses, something the Senate is expected to decide on Friday. Earlier on Thursday, Mr. Schiff proposed that the Senate call witnesses but limit depositions to one week, as was done during the impeachment trial of President Bill Clinton.

Wrapping up his response to Ms. Warren’s question, Mr. Schiff said: “I think the country deserves a fair trial. And yes, senator, if they don’t get that fair trial, it will just further a cynicism that is corrosive to this institution and to our democracy.”

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