(Bastien Inzaurralde/The Washington Post)

The White House on Tuesday reiterated President Trump’s false contention that he lost the national popular vote because of 3 million to 5 million illegal votes, as yet another untruth swelled into a distraction that threatens to undermine his first week in office.

Trump repeatedly has claimed there was widespread voter fraud in the November election, most recently telling congressional leaders on Monday night that he thinks it is why he lost the popular vote to Democratic candidate Hillary Clinton. Although the president’s theory has been broadly discredited, White House press secretary Sean Spicer held up debunked research Tuesday to support it and left open the possibility of a federal investigation.

“The president has believed that for a while based on studies and information he has,” Spicer said. When pressed, Spicer would not state whether he personally agrees with Trump, only that it is the president’s “long-standing belief.”

As a candidate, Trump played fast and loose with the facts, frequently exaggerating and peddling falsehoods — or in some cases lying — to promote himself and undermine his adversaries. As president, Trump’s behavior has not been much different. He is alleging voter fraud on such a large scale that, if true, it would amount to a massive scandal. He and Spicer also overstated the size of last Friday’s inauguration crowd despite clear evidence to the contrary.

Trump has been fixated on his public image and preoccupied with doubts about his legitimacy as president, which advisers say he has found frustrating and demoralizing.

President Trump, right, welcomes Senate Majority Leader Mitch McConnell, (R-Ky.), center, and Senate Minority Leader Charles E. Schumer (D-N.Y.), left, at a White House reception on Monday night. (Ron Sachs / Pool/EPA)

If Trump is worried whether losing the popular tally by nearly 3 million votes could snarl his legislative agenda, his allies say he need not be concerned: His party controls Congress, and Trump’s legislative agenda is being treated by Republicans as if he had won a sweeping mandate and enjoyed high approval ratings.

But Republican strategists argue that Trump has not psychologically adjusted to becoming president and that he risks eroding his stature and damaging his credibility if he continues to assert falsehoods under the microscope of the White House.

“You don’t want to be a president whose word trades at a discount rate — and when it comes to measures of his personal popularity, President Trump’s words seem to trade at a discount rate,” said Ari Fleischer, a White House press secretary under former president George W. Bush.

On Monday night at a White House reception for congressional leaders, Trump privately told lawmakers that he would have won the popular vote had it not been for 3 million to 5 million illegal votes, according to people familiar with the conversation.

But elections officials in most states — many of them Republican — have reported no instances of widespread election problems, including fraud.

Despite Trump’s repeated claims, his own campaign’s attorneys stated in a recent court filing: “All available evidence suggests that the 2016 general election was not tainted by fraud or mistake.”

Sen. Bernie Sanders (I-Vt.), right, and Senate Minority Leader Charles E. Schumer (D-N.Y.) speak to journalists after a Senate Democratic Caucus luncheon on Tuesday. (Melina Mara/The Washington Post)

Democrats fear that Trump’s allegations of voter fraud are about more than his ego. They say he might be signaling support for a systematic Republican effort in the states to suppress voting rights.

“When Trump talks about 3 [million] to 5 million people voting illegally, he is sending a message to every Republican governor in this country to go forward with voter suppression,” said Sen. Bernie Sanders (I-Vt.), who caucuses with the Democrats.

Senate Majority Leader Mitch McConnell (R-Ky.) was asked about Trump’s claims, he would not say whether he agrees, only that he believes voter fraud is a problem generally around the country.

“Most states have a done a better job on this front, but the notion that election fraud is fiction is not true,” said McConnell, who like many Republicans has voiced support for voter ID laws.

Michael Waldman, president of the Brennan Center for Justice at the New York University School of Law, accused Trump of pushing “fake news about our democracy.”

“It is unprecedented in the country’s history for the president and the White House spokesman to push a lie of this magnitude about voting,” Waldman said in a statement. “These are not random conspiracy theorists on the Internet. These are the highest officials in the land.”

Trump’s fact-challenged brush fires are creating awkwardness for his supporters on Capitol Hill, where many Republicans are unwilling to second his unsubstantiated claims but also are taking pains to not be seen as rebuking the president.

On Tuesday, lawmakers were visibly uncomfortable when asked whether they agree with Trump’s theory.

“I can’t tell Donald — uh, President Trump how to speak or what he wants to focus on,” said Sen. Marco Rubio (R-Fla.), catching himself being too casual with titles. “I don’t agree with that. And if there’s evidence of that, it should be investigated.”

Other senators refused to engage on the subject.

“I don’t think about it,” Sen. Tim Scott (R-S.C.) said. “It’s not important to me.”

A few took Republicans took a harder line. Sen. Lindsey O. Graham (R-S.C.), long a thorn in Trump’s side, told CNN that the president’s allegations were undermining faith in the democratic system.

“I would urge the president to knock this off,” Graham said. “This is the greatest democracy on Earth. We’re the leader of the free world. And people are going to start doubting you as a person if you keep making accusations against our electoral system without justification.”

From the earliest days of his campaign, Trump has been infatuated by his crowd sizes. He tweeted Tuesday that he would hang a panoramic photograph of his inaugural crowd, given to him by a supporter, on a wall of the West Wing.

Trump’s focus on numbers is a holdover from his decades as a marketer and businessman, when he would toss around figures for his personal wealth or the value of his buildings or the ratings of his television shows as validations of the power of his brand.

“It’s a combination of ego and a successful track record of always marketing everything he’s done in his business as ‘the biggest,’ ‘the best,’ ‘the superlative,’ ” Fleischer said. “It’s just ingrained in him.”

Fleischer likened Trump to the dragon in J.R.R. Tolkien’s fantasy work “The Hobbit.” It flies around and is all-powerful, nearly covered in armor save for one unarmored patch. Trump’s unarmored patch, he posited, is his obsession with proving his personal popularity.

“One well-placed arrow can take him down,” he said.

Correction: Fleischer, in his comparison, likened Trump to a dragon he described as from “The Lord of the Rings” series, but the dragon he describes was from another related Tolkien work, “The Hobbit.” The reference above has been corrected.