The committee's work has been deeply, and perhaps irreparably, undermined by Nunes' apparent coordination with the White House.
Jones said Nunes should "Absolutely" step aside from the position of committee chairman. Tuesday, the lawmaker said there is not need to recuse himself from the investigative proceedings.
The California Republican, who was a member of Trump's presidential transition team, has said he met with a secret source last week on White House grounds to review classified material that showed Trump associates' communications had been captured in "incidental" surveillance of foreigners in November, December and January.
During a brief White House photo op, Trump said he felt "somewhat vindicated" by Nunes' revelation since FBI Director Comey and other high ranking officials, including Nunes, had said a Trump tweet claiming former President Obama had ordered wiretapping of Trump Tower during the 2016 campaign was not true.
But Schiff argued it was up to Nunes to restore credibility in the committee's investigation.
Schiff, House Minority Leader Nancy Pelosi and other top Democrats have called for Nunes to recuse himself from the Russian Federation investigation.
In the Senate, the top Republican and Democrat on the intelligence committee said Wednesday they would cooperate and steer clear of politics in their panel's probe.
The White House denied it had a hand in halting the hearing, saying it welcomed Yates' testimony.
If so, Schiff said, he wants to know: "Why weren't they presented in a more transparent way to the committee?"
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"There is no letter from the White House because Yates attorney's letter clearly states a non-response will be seen as the White House not asserting executive privilege", the official said.
The canceled hearing would have been the first opportunity for the public to hear Yates' account of her role in the firing of Trump's first national security adviser, Michael Flynn.
Unfortunately for Nunes, it is no longer just the Democrats' problem.
The committee leaders were trying to agree on a common set of initial witnesses, Schiff said, an issue that prompted the cancellation of both an open and closed hearing this week.
"I believe that the Chairman should recuse himself from any further involvement in the Russian Federation investigation, as well as any involvement in oversight of matters pertaining to any incidental collection of the Trump transition, as he was also a key member of the transition team", Schiff said.
"My colleagues are perfectly fine".
Spicer's comments come as the leaders of the House intelligence committee are trying to get their Russian Federation investigation back on the rails, according to Schiff. They made a point of putting themselves at arm's length from the partisanship and disputes surrounding the House investigation.
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.