This week, Donald Trump told members of Congress that he would have won the popular vote, were it not for 3 to 5 million votes cast against him by "illegals." And when asked about it at the Tuesday press briefing, White House press secretary Sean Spicer affirmed that "the president does believe that."

But there is no evidence.

No, you're not having deja vu. Yes, he has made this claim before. Yes, many outlets (NPR included) fact-checked it.

And other high-profile Republicans have not come to Trump's aid in defending his voter-fraud claims.

"I've seen no evidence to that effect. I've made that very, very clear," House Speaker Paul Ryan told reporters, according to The Hill.

South Carolina Sen. Lindsey Graham on Tuesday offered a sharper rebuke, saying that he wants Trump to either say that the election was fair, or provide evidence that it was not.

"I am begging the president, share with us the information you have about this or please stop saying it," he said, adding:

"As a matter of fact, I'd like you to do more than stop saying it; I'd like you to come forward and say, 'Having looked at it, I am confident the election was fair and accurate, and people who voted voted legally.' ... If he doesn't do that, this is going to undermine his ability to govern this country."

In the era of persistent misinformation and conspiracy theories — some of them repeated by the president himself — repeating the (non-alternative) facts is important. So here's a run-through our fact check again, starting with some bold typeface:

The Trump team has yet to provide evidence of widespread voter fraud.

Back in November, Donald Trump tweeted something similar to what he told lawmakers this week, saying (without providing evidence) that he "won the popular vote if you deduct the millions of people who voted illegally." He later also alleged, once again without evidence, that there was "serious voter fraud" in three states.

Those are some heavy accusations. When asked for evidence shortly thereafter, Jason Miller, a senior communications adviser for Trump's campaign, did provide two sources. However, those proved to have some major problems.

One, an analysis of survey data published on the Washington Post's social-science blog, Monkey Cage, estimated that "6.4 percent of non-citizens voted in 2008 and 2.2 percent of non-citizens voted in 2010." However, that study drew heavy criticism from other scholars, who both saw weaknesses in the authors' methods and the survey they used.

In addition, one of the authors of that heavily criticized study himself later rejected attempts to use that study to prove fraud.

"On the right there has been a tendency to misread our results as proof of massive voter fraud, which we don't think they are," wrote Old Dominion University political science professor Jesse Richman in a blog post.

In another post, he further pointed out that even if one did extrapolate from his study, it does not imply that illegal votes would have affected the outcome of the 2016 presidential election, because it simply was not a close election. Though Trump won the electoral vote, Hillary Clinton won the popular vote by nearly 3 million votes.

Miller also cited a 2012 Pew Charitable Trusts report on the state of states' voting systems. And that report did reveal some troubling statistics. For example, it found that 2.8 million people are registered to vote in more than one state and that 24 million registration records "are estimated to be inaccurate or no longer valid."

That means voting systems could definitely be modernized in some ways.

However, that is not at all evidence of fraudulent voting, as the study's main author pointed out on Twitter (highlighted by the Washington Post's Fact Checker):

And importantly, while voting systems could be (and have been) improved more, there are rules in place that keep people from being quickly purged from registration lists — simply moving from one state to another or dying won't instantaneously remove a person from the list.

"So what has happened is that this notion that voter registration lists can possibly be 100 percent accurate at any point in time is a complete fiction," Lorraine Minnite, author of The Myth of Voter Fraud, told NPR in November. "It's not allowed under federal law to be that way."

This is not to say that voter fraud doesn't happen; it does. However, it is not widespread.

Bigger problems to come?

Trump's willingness to make (and repeat) untrue claims, demonstrated in just the first few days as president, have provided a taste of the challenges the media could face in holding the administration accountable in the coming years.

As I wrote in September, repeated false claims create a difficult situation for journalists. On the one hand, we could continue to write refutations every time one of these inaccuracies is repeated — but that means repeating an untrue claim. On the other hand, we could refuse to repeat the claim — but that means allowing one of the most powerful voices in the nation to make the claim repeatedly unchecked.

Aside from the voter-fraud remarks, press secretary Spicer gave other false statements about the inauguration over the weekend. Photos of the National Mall from 2009 and 2017 clearly show Obama's first inauguration with far more attendees. To explain the lower attendance at the Trump inauguration, Spicer made untrue claims about Mall ground coverings and inauguration security, offering ready-made explanations for that attendance to anyone who wants them. He also later said he was referring to audience overall, including online streaming of the event.

And for anyone who is firmly dug into their positions, those positions can be remarkably immovable. Beliefs, as political scientist Brendan Nyhan wrote in a 2016 paper, "seem to be closely linked to people's worldviews and may be accordingly difficult to dislodge without threatening their identity or sense of self."

Copyright 2017 NPR. To see more, visit http://www.npr.org/.

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