The former press secretary for Hillary Clinton Hillary Diane Rodham ClintonHillicon Valley: FBI chief says Russia is trying to interfere in election to undermine Biden | Treasury Dept. sanctions Iranian government-backed hackers The Hill's Campaign Report: Arizona shifts towards Biden | Biden prepares for drive-in town hall | New Biden ad targets Latino voters FBI chief says Russia is trying to interfere in election to undermine Biden MORE’s presidential campaign says White House press secretary Sean Spicer should have resigned rather than claim that President Trump Donald John TrumpHR McMaster says president's policy to withdraw troops from Afghanistan is 'unwise' Cast of 'Parks and Rec' reunite for virtual town hall to address Wisconsin voters Biden says Trump should step down over coronavirus response MORE drew a bigger inauguration crowd than former President Obama.

The Trump team's insistence that the media was misreporting the crowd estimate caused tension between Spicer and the press on Sunday, which Brian Fallon seized on.

“There’s clear intent. It was a lie. It should be called a lie. And if he was put in the situation by [White House chief of staff] Reince Priebus or his boss, Donald Trump, to go out and tell a lie to the American people, he should have resigned rather than go out and take the podium,” Fallon told CNN’s “Reliable Sources.”

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Spicer in his first press briefing on Saturday blasted the media for its coverage of the inauguration crowd.

"This was the largest audience to ever witness an inauguration, period, both in person and around the globe,” he said.

Pictures emerged throughout Friday comparing the crowd at Obama’s 2009 inauguration to that of Trump’s.

White House counselor Kellyanne Conway said early Sunday that Spicer’s claim was an example of “alternative facts.”

“You’re saying it’s a falsehood. And they’re giving, Sean Spicer, our press secretary, gave alternative facts to that,” Conway told NBC’s “Meet the Press” early Sunday.

Fallon, when asked by host Brian Stelter if he would have resigned, said he has never been put in such a position.

“But I’d like to think that if I ever was, I would have too much integrity to go out and look in the cameras and say something that was provably false,” he said.