Donald Trump, having propelled his presidential campaign to victory while often disregarding the truth, now is testing the proposition that he can govern the country that way.

In the first five days of his presidency, Trump has put the enormous power of the nation’s highest office behind spurious – and easily disproved – claims.

He began with trivial falsehoods about the size of the crowds at his inauguration but has since escalated a more grave claim that undermines the trustworthiness of the nation’s electoral system. In a White House reception Monday night for congressional leaders, Trump alleged that as many as 5 million undocumented immigrants voted in the 2016 election, denying him a popular-vote majority.

It was a claim that Trump had made in the aftermath of the election, with no evidence to back it up. As unsettling as that was in a president-elect, the implications are far greater when something clearly untrue is spread by a commander in chief – and when the weight and resources of his administration are brought to bear in amplifying such information.

White House press secretary Sean Spicer, whose own credibility has been undercut during his first week on the job, offered no verifiable evidence Tuesday to back up the president’s claim.

“The president does believe that,” Spicer said. “He has stated that before. I think he’s stated his concerns of voter fraud and people voting illegally during the campaign, and he continues to maintain that belief based on studies and evidence that people have presented to him.”

Beliefs, however, are not the same as facts. Pressed to produce that evidence upon which Trump bases his assertion, Spicer said that a 2008 study by the Pew Charitable Trusts “showed 14 percent of people who voted were noncitizens. There’s other studies that have been presented to him. It’s a belief he maintains.”

Pew made no such finding. Its study, it has noted, was issued in 2012 and dealt with inaccurate, outdated voter registration rolls. It did not address large-scale voter fraud.

Trump’s attraction to conspiracy theories and his contempt for facts that tarnish his pride may have serious implications for his ability to govern.

At the California State Capitol on Tuesday, Democratic Gov. Jerry Brown, used his annual State of the State address to criticize the new president for his refusal to tether himself to the facts.

“Above all else, we have to live in the truth,” Brown said. “When the science is clear or when our own eyes tell us that the seats in this chamber are filled or that the sun is shining, we must say so, not construct some alternate universe of non-facts that we find more pleasing.”

Trump allies – and adversaries – had hoped that with his inauguration, he would leave behind the hyperbolic reality-show culture that made him a celebrity. In the late stages of his presidential campaign, Trump had disavowed his years-long promotion of the racially tainted falsehood that Barack Obama, the nation’s first African-American president, was born outside the United States and therefore an illegitimate president.

But the first days of his presidency show that, for Trump, old reflexes are hard to change.

Veterans of previous White Houses say they can recall no precedent for what Trump and his top aides are doing. They worry about the implications of this untethering from the truth when big decisions must be made about dealing with terrorism or charting the course of the economy.

“The degree to which they are creating their own reality, the degree to which they simply make up their own scripts, is striking,” said Peter Wehner, a Trump critic who was a top strategist in the George W. Bush White House. “It’s a huge deal, because in the end you really can’t govern, and you can’t persuade people, if you do not have a common basis of fact.”

Former Arkansas governor Mike Huckabee, who was a stalwart Trump supporter, told Fox Business Network on Tuesday that he was mystified by Trump’s claim about illegal voters – and by his motivations for bringing it up.

“I have no evidence whatsoever, and I don’t know that anyone does, that there are that many illegal people who voted,” Huckabee said. “And frankly it doesn’t matter. He’s the president, and whether 20 million people voted, it doesn’t matter anymore.”

Sen. Lindsey Graham, R-S.C., said that Trump’s claim “undermines faith in our democracy. It’s not coming from a candidate for office. It’s coming from the man who holds the office. So I am begging the president, share with us the information you have about this, or please stop saying it.”

What made Trump’s claim more exasperating to fellow Republicans was that it had come as his new administration seemed to be getting back on track after a set of embarrassments during its first weekend.

On Saturday, the new president stood at CIA headquarters, before a wall of stars memorializing slain officers, and said that a dishonest media had refused to report the true size of the crowd on the Mall for his inauguration. Trump offered his own estimate of “a million, a million and a half people.”

Later that day, he dispatched Spicer to the White House briefing room, where the press secretary – in his first formal encounter in that setting with the reporters who cover the president – rattled off another round of unproved figures and contended that the crowd represented “the largest audience to ever witness an inauguration, period – both in person and around the globe.”

On Sunday, White House counselor Kellyanne Conway compounded the damage in a contentious interview with NBC’s “Meet the Press” in which she said: “Sean Spicer, our press secretary, gave alternative facts.”

Show moderator Chuck Todd responded: “Alternative facts aren’t facts. They are falsehoods.”

Until Trump’s comments Monday night about illegal voters, it had appeared that the new administration might be regaining its footing after that wobbly start.

During the day, Trump signed a set of executive orders and stayed on message during meetings with leaders from business and organized labor. Spicer had handled his Monday briefing with aplomb, taking questions from reporters for more than an hour.

The failure by Trump and his team to maintain that discipline will do long-term damage, said Matthew Dowd, who was the chief strategist for George W. Bush’s 2004 re-election campaign. “I don’t think he realizes how much he is hurting himself.”

Then again, Trump may well believe that this is the style which brought him to the White House, in defiance of every expectation. Americans knew what they were getting when they elected him.