WASHINGTON – A USA TODAY/Suffolk University Poll has sobering findings for President Donald Trump: Most Americans don't believe his denials that his campaign colluded with Russians in the 2016 campaign.

Prosecutors continue to file court documents and plea deals in cases involving some of the president's closest associates, including his former personal lawyer Michael Cohen, who was sentenced last week to three years in prison.

More than a third of those surveyed express "some" trust in Trump's version of events. Nearly six in 10 have little or none.

The skepticism toward Trump sets a rocky landscape for him even before special counsel Robert Mueller submits a report, perhaps soon, that will examine whether Trump's team conspired with the Russians and if the president tried to obstruct investigations into those accusations.

Some of those surveyed said they don't need to wait for a report.

"I have plenty of evidence that the president lied ... starting with the first day of his inauguration with the crowd size," said Thomas Maslany, 72, a retired engineer from Perkiomenville, Pennsylvania, who voted for Democrat Hillary Clinton in 2016. Trump inaccurately boasted that he drew a record crowd to the National Mall for his swearing-in. "I know the president's a liar," Maslany said, "and I've found no evidence that Mueller is a liar."

Most of those surveyed, 53 percent, say they have a lot or some trust in Mueller; 38 percent have little or no trust in the former FBI director and his investigation to be fair and accurate. In contrast, 59 percent express little or no trust in the president's denials; 35 percent say they have some or a lot of trust in him to speak the truth.

Trump has a core of unwavering supporters who endorse his argument that the Mueller investigation is a "witch hunt." The proportion who say they have "a lot of trust" in the president's denials hasn't budged since March: 24 percent then, 24 percent now.

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Jeff Jacob, an insurance salesman and Trump supporter from Corona, California, called the Mueller inquiry "a waste of time" and a case of payback from the political establishment.

"They're doing whatever they can to stick him," he said in a follow-up phone interview, though he acknowledged he doesn't like some of the things the president said. "He shoots his mouth off, but that's probably one of the reasons I voted for him."

Fifty percent say Russians "definitely" interfered in the election to help Trump; 27 percent say they definitely didn't. Nearly as many, 46 percent, say Trump associates "definitely" colluded with the Russians; 29 percent say they definitely didn't.

"I don't think they changed votes (in voting machines); I think they changed minds, and that eventually may have changed votes," Arlanna Spencer, 43, a stay-at-home mother from Flagler Beach, Florida, said of the Russians. She is a Democrat who voted for Clinton in 2016. "They definitely manipulated people."

The poll of 1,000 registered voters, taken by landline and cellphone Tuesday through Sunday, has a margin of error of +/-3 percentage points.

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Headlines in the Russia case continue to erupt.

Trump's former White House national security adviser, Michael Flynn, was scheduled to be sentenced for lying to the FBI on Tuesday morning. "Good luck in court to General Michael Flynn," the president tweeted Tuesday morning. "Will be interesting to see what he has to say, despite tremendous pressure being put on him, about Russian Collusion in our great and, obviously, highly successful political campaign. There was no Collusion!"

Americans are watching. Almost half of those polled say they pay "a lot" of attention to the Russia story; 36 percent pay "a little" attention. Fourteen percent express no interest.

Those who follow the news most closely are the most skeptical. Among those, two-thirds, 66 percent, have little or no trust in Trump's denial. Nearly six in 10, 59 percent, say the Russians "definitely" interfered to help Trump. A solid majority, 56 percent, say they are convinced Trump associates colluded with the Russians.

"The people who are following the investigation a lot tend to lean more Democratic and find it useful and gratifying to see new allegations, plea deals and indictments," said David Paleologos, director of the Suffolk University Political Research Center. "Those who are not following the investigation closely are Trump supporters, in large part, and don't buy it. They are invested in Trump's success and are pained to watch his stock declining day after day with every new indictment."

Mueller, who hasn't responded publicly to Trump's frequent attacks in interviews and on Twitter, has a favorable-unfavorable rating of 39 percent-31 percent. His unfavorable rating has risen over the year, up from a 37 percent-23 percent rating in the USA TODAY/Suffolk Poll in March.

Views of Mueller are in positive territory by a net 8 percentage points. Trump has a favorable-unfavorable rating of 40 percent-57 percent, in negative territory by 17 points.

Catherine O'Connor, 63, an artist from Lockport, New York, and a political independent who voted for Clinton in 2016, accused Trump of being unethical and praised Mueller as the right person for a difficult time. "He's like Superman in a business suit: Truth, justice and the American way," she said.