Without witnesses, Republicans, who control the Senate, say the trial could end as early as Friday with Trump's acquittal, which would leave him in office and allow him to claim vindication just as the Democratic Party holds its first nominating contest for the Nov. 3 election in Iowa on Monday.
Trump will hold a rally in the state on Thursday night.
Democrats accuse the Republican president of abusing his power by using congressionally approved military aid as leverage to get a foreign power to smear former Vice President Joe Biden, a leading contender for the Democratic nomination.
The Democratic-led House of Representatives approved the two articles of impeachment in December. Lawyers for Trump and the House Democrats who are managing the prosecution in the Senate trial will spend Thursday answering questions from lawmakers, read aloud by U.S. Chief Justice John Roberts.
On Friday, each side was expected to present what amount to closing arguments before the Senate moves to the central question of whether to call witnesses, which Democrats believe is essential to shed more light on Trump's attempt to persuade Ukraine President Volodmyr Zelenskiy to investigate Biden.
Democrats are unlikely to muster the two-thirds majority needed to remove Trump from office no matter what happens, but allowing witnesses could inflict political damage on the president as he seeks re-election.
Republican Senator Josh Hawley said he sensed the Republicans had enough votes to defeat a motion to call witnesses and that the rules for the trial called for a "pretty quick transition" to a vote on acquittal afterward.
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