WASHINGTON (REUTERS) - Democrats appeared to have fallen short on Thursday (Jan 30) in their bid to secure the votes needed to call witnesses in President Donald Trump's impeachment trial, clearing the way for Mr Trump's likely acquittal as early as this weekend.

Democrats had urged a handful of Republicans to support their effort to call witnesses, but their hopes appeared dashed when Republican Senator Lamar Alexander, who had been undecided, declared further evidence in the case was unnecessary.

"There is no need for more evidence to prove something that has already been proven and that does not meet the United States Constitution's high bar for an impeachable offence," Mr Alexander said in a statement after the evening session had concluded.

Barring an unforeseen change of heart by another Republican senator, it appeared Mr Alexander's decision would bring an end to Mr Trump's two-week trial and provide him with the swift decision he had sought.

Earlier, Republican Senator Susan Collins broke with her party and announced her support for witnesses. But Democrats needed at least of three of her colleagues to defect and give them the 51 votes needed to call witnesses and prolong the trial.

Two-thirds of the Senate is required to remove Mr Trump from office. He is unlikely to be convicted.

Democrats had hoped to hear from former national security adviser John Bolton after a report - which he has not denied - that he planned to say in an upcoming book that Mr Trump told him he wanted to freeze US$391 million (S$532.5 million) in US military aid for Ukraine until it investigated Democratic presidential contender Joe Biden and his son Hunter, who worked for a Ukrainian energy firm while his father was vice-president.

The Democratic-controlled House of Representatives impeached Mr Trump in December, formally accusing him of abusing his power for pressuring Ukraine to investigate the Bidens. The House also charged Mr Trump with obstruction of Congress.

Mr Trump's acquittal would allow him to claim vindication just as the Democratic Party holds its first nominating contest for the Nov 3 election in Iowa on Monday.

Mr Trump held a rally in Des Moines, Iowa, on Thursday night and slammed the trial, calling it an effort by Democrats to overthrow his 2016 election victory.

"They want to nullify your ballots, poison our democracy and overthrow the entire system of government," he said.

TRYING TO UNMASK WHISTLE-BLOWER

The two sides also sparred over the unnamed government official whose whistle-blower complaint about Mr Trump's dealings with Ukraine spurred the drive to remove him from office.

Mr Trump and some other Republicans have pressed for months to unmask the intelligence official who filed the report and have tried to paint that person as a partisan figure working with Democrats to destroy Mr Trump's presidency.

The government has provided security to the whistle-blower in response to security threats, according to the person's lawyers.

On Thursday, the issue boiled to the surface again when US Chief Justice John Roberts, who is presiding over the trial, refused to read a question from Republican Senator Rand Paul that included the name of a person that right-wing media have accused of being the whistle-blower. Mr Paul is one of several Republicans, including Mr Trump, who have posted social media links to some of those news articles.

"The presiding officer declines to read the question as submitted," Mr Roberts said. He had rejected a similar question the day before.

Mr Paul said his question, which asked whether that person worked with a member of Democratic Representative Adam Schiff's staff to impeach Mr Trump, was not meant to unmask the whistle-blower.

"My question's not about the whistle-blower. My question's about two people who are friends," he told reporters.

Democrats disagreed.

"This question was really framed and intended to expose the identity of the whistle-blower and subject that whistle-blower to retaliation," Democratic Senator Richard Blumenthal told reporters.

Mr Bradley P. Moss, a lawyer whose firm represents the whistle-blower, called the Republican effort "a stain on the legacy of this constitutional republic".

CLOSING ARGUMENTS, AND CLIMACTIC VOTE

On Friday, each side is expected to present closing arguments before the Senate moves to the question of whether to call witnesses.

If the vote on whether to allow witnesses is 50-50, Mr Roberts could step in to break the tie. But there is so little precedent for impeachment trials - this is only the third of a president in US history - that Senate aides said there was no way to know exactly what would occur.

If Mr Roberts declines to break a tie, the vote deadlock would mean a defeat for Democrats.

Mr Schiff, the lead Democratic prosecutor in the trial, proposed both sides conduct closed-door witness depositions for a week while the Senate returns to normal business.

But there was no sign his plea was being considered by Republicans.