(Adds poll results, TV ratings)
By David Morgan and Doina Chiacu
WASHINGTON, Jan 22 (Reuters) - Democrats accused President Donald Trump at his impeachment trial on Wednesday of a corrupt scheme to pressure Ukraine to help him get re-elected and warned that America's global prestige would suffer if the U.S. Senate acquits him.
The Republican Trump sounded a defiant note, telling reporters in Switzerland the Democrats did not have enough evidence to find him guilty and remove him from office.
In a two-hour opening argument for the prosecution after days of procedural wrangling, U.S. Representative Adam Schiff said Trump had pushed Ukrainian President Volodymyr Zelenskiy to investigate former Vice President Joe Biden and Biden's son on unsubstantiated corruption charges last year.
"To implement this corrupt scheme, President Trump pressured the president of Ukraine to publicly announce investigations into two discredited allegations that would benefit President Trump's 2020 presidential campaign," Schiff said.
Democrats argue that Trump was trying to find dirt on Biden, a leading contender for the Democratic presidential nomination for the November election, and his son Hunter Biden who had served on the board of a Ukrainian gas company, to help the president win a second term.
Trump was impeached last month by the Democratic-controlled House of Representatives on charges of abuse of power and obstruction of Congress for his dealings with Ukraine and impeding the inquiry into the matter.
A Reuters-Ipsos poll released on Wednesday found a bipartisan majority of Americans wanting to see new witnesses testify in the impeachment trial.
It said about 72% agreed that the trial "should allow witnesses with firsthand knowledge of the impeachment charges to testify," including 84% of Democrats and 69% of Republicans.
Trump denies any wrongdoing and his fellow Republicans in the Senate say his behavior does not fit the description of "high crimes and misdemeanors" outlined in the U.S. Constitution as a reason to oust a U.S. president.
Trump is almost certain to be acquitted by the Republican-controlled 100-member Senate, where a two-thirds majority is needed to remove him from office. But the trial's effect on his re-election bid is unclear.
The case against him is focused on a July 25 telephone call in which he asked Zelenskiy to open a corruption investigation into the Bidens as well as a discredited theory that Ukraine, not Russia, meddled in the 2016 U.S. election.
"Nothing could be more dangerous to a democracy than a commander in chief who believed that he could operate with impunity, free from accountability. Nothing, that is, except a Congress that is willing to let it be so," said Schiff, who is leading the prosecution team of Democratic "managers" from the House.
Making references to 18th century U.S. founding father Alexander Hamilton and the late Republican President Ronald Reagan, Schiff said the world was watching.
"For how can any country trust the United States as a model of governance if it's one that sanctions precisely the political corruption and invitation to foreign meddling that we have long sought to eradicate in burgeoning democracies around the world?"
He said senators would "also undermine our global standing" if they did not oust Trump three years into his tumultuous presidency.
Democrats have up to three days to make their case. Trump's defense team will have three days after that for rebuttal in a trial that could potentially conclude next week.
Tuesday's start of the impeachment trial drew about 11 million TV viewers, according to Neilsen ratings data, a figure that fell short of the roughly 13.8 million who watched last November for the first day of the House impeachment inquiry into Trump.
It is the third presidential impeachment trial in U.S. history. The opening days have been dominated by arguments over Democratic requests for more witnesses and records.
The Trump administration has not complied with subpoenas for documents and has urged officials like former national security adviser John Bolton and Secretary of State Mike Pompeo not to participate in the impeachment investigation.
In Davos, Switzerland, Trump told reporters at the World Economic Forum that he was happy with the way the trial was going.
"I thought our team did a very good job. But honestly, we have all the material. They don't have the material," Trump said.
Democratic U.S. Representative Val Demings, one of the House impeachment managers, said Trump's comment amounted to boasting about obstruction of Congress.
"This morning, the president not only confessed to it, he bragged about it: 'Honestly, we have all the material. They don't have the material,'" she said.
But a senior administration official, asked to explain what Trump was referring to, said: "What he's clearly saying is we have all the facts on our side, and those facts prove he's done nothing wrong."
Trump said allowing Bolton to testify at the trial would present national security concerns.
"He knows some of my thoughts, he knows what I think about leaders. What happens if he reveals what I think about a certain leader and it's not very positive?" Trump said.
Bolton, a foreign policy hawk who was fired by Trump last year, has disdainfully described the Ukraine pressure campaign as a "drug deal" and testimony from him could be awkward for the president.
A parade of current and former officials spoke at House impeachment hearings last year of a coordinated Trump effort to pressure Ukraine.
But those televised hearings did little to change support for and against Trump's impeachment. Reuters/Ipsos polling since the inquiry began shows Democrats and Republicans responding largely along party lines.
Trump and his legal team say there was no pressure and that the Democrats' case is based on hearsay aimed at overturning Trump's 2016 election win.
(Reporting by Doina Chiacu and David Morgan; Additional reporting by Richard Cowan and Susan Heavey; Writing by Alistair Bell and Steve Holland; Editing by Andy Sullivan, Howard Goller and Peter Cooney)
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