Top Democrats in the House have already called on Nunes's to recuse himself from the panel's investigation into Russian interference in the 2016 election, which includes a probe into possible coordination between the Trump campaign and Russian operatives whom US intelligence chiefs credit with last summer's infiltration of Democratic National Committee servers.
But last week's hearing - the first and so far only public hearing of the House Russia investigation - sparked a wildfire of partisan fighting after FBI Director James Comey confirmed he is investigating possible coordination between President Donald Trump's campaign aides and Russian officials. He also admitted visiting the White House before he made this announcement.
Questions over Nunes' independence have split the usually non-partisan Intelligence Committee as Democrats accuse Republicans of trying to damage the investigation.
TRT World's Tetiana Anderson has more on the controversy from Washington DC.
Nunes said initially at his press conference that he had seen materials that "clearly show the president elect and his team were at least monitored" during the transition.
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"Whether the White House's desire to avoid a public claim of executive privilege to keep her from providing the full truth on what happened contributed to the decision to cancel today's hearing, we do not know", Schiff said in statement Tuesday morning.
"This is what cover-up behavior looks like", he said.
Upon finding the documents, Nunes said he copied their identifying numbers so he could formally request them for the rest of his committee to view. Yet when asked whether he would continue to lead the committee's investigation, Nunes asked, "Well, why would I not?"
Pressed by reporters as to how Mr Nunes had obtained clearance to enter the White House Mr Spicer said he had no new information regarding the meeting between the Republican congressman and the source.
But the main reason Democrats are mad at Mr. Nunes is because he's raising an issue they'd rather avoid-to wit, that he's seen documents showing that US intelligence agencies may have "incidentally" collected information about people connected to Mr. Trump.
CNN has reached out to Nunes for comment on the meeting and has not yet received a response.
"The American people should have had the benefit of an open hearing", Schiff said, noting the the initial public hearing brought Comey's acknowledgment that the FBI was investigating possible collusion between Trump campaign figures and Russian Federation.
Nunes and the congressional inquiry he's leading into alleged Russian interference have come under increasing criticism in recent days, after he first claimed he had discovered "concerning" evidence that the Trump campaign was monitored after the election.
Yates served as acting attorney general in the early days of the Trump administration until she was sacked for refusing to implement President Donald Trump's order barring travelers form seven Muslim-majority countries.