Republicans revealed they have a "weak hand" in the shutdown fight on Tuesday by clinging to an "easily debunked lie" about the government funding bill during media interviews, according to one analyst.

Dan Pfeiffer, former senior advisor to President Barack Obama, discussed the government shutdown, which began on Wednesday, during a new episode of "Pod Save America." He argued that Republicans "looked stupid" for clinging to the "lie" that Democrats are seeking to provide free health care to immigrants in the funding bill in many of their media interviews.

"It seems like the Republicans are desperate to hang on to this very easily debunked lie about this idea that somehow this entire shutdown is that the Democrats want to shut the government down to give free health care to undocumented people, when in fact the Affordable Care Act says in law in writing that you absolutely cannot do that," Pfeiffer said.

"For all of their swagger and confidence in the pages of Punch Bowl and Politico, the way the Republicans are acting suggests they think they may have a weak hand because if you have a strong hand, then you don't dine out on this lie the whole time," he added.

Pfeiffer also argued that the claims Republicans are making about the shutdown seemed to crumble when they faced pushback from media outlets that don't align with the right wing.

"They looked stupid," Pfeiffer said. "I think many of them just believed that that was actually the case without fully understanding it."