Washington (CNN) The latest round of political finger-pointing over the House Intelligence Committee's investigation into Russia's meddling in the US elections is threatening to undermine the bipartisan committee's work.

Chairman Devin Nunes of California and ranking Democrat Adam Schiff, also of California, on Friday held dueling news conferences for the second time this week. At his event, Nunes announced he was postponing next week's public hearing on the Russia investigation, prompting a Democratic member to call for his ouster.

"I don't see how they go forward working together the way it's going," one senior Democratic congressional aide said. "Maybe they'll find a way to recover, but I'm skeptical."

The House and Senate intelligence committees historically have been a bipartisan staple of Capitol Hill, with members conducting their work together and mostly in private. But the Russia investigation has become a political firestorm surrounding questions of whether Trump's associates colluded with the Russians to help the GOP candidate during the election campaign, and it risks ripping the committee apart.

A Democratic intelligence committee source told CNN that Nunes' move to postpone the hearing on Friday was a "suicide bomb" that signaled Nunes was effectively trying to destroy the Russia investigation.

Nunes said he was only postponing the hearing -- where former Director of National Intelligence James Clapper, former CIA Director John Brennan and former acting Attorney General Sally Yates were slated to testify -- to a later date. But Democrats accused him of canceling it.

Democrats were already seething over Nunes' decision Wednesday to brief the White House and tell the media that he had obtained intelligence suggesting President Donald Trump's communications may have been intercepted by intelligence agencies -- before telling his own committee members. Nunes later apologized for the move, which Democrats said was a major breach of protocol.

On Fox News' "Hannity" Thursday evening, Nunes said he "felt like I had a duty and obligation" to brief Trump on the intelligence, because "he's been taking a lot of heat in the news media."

House Democrats amplified their calls on Friday for an independent commission to investigate Russia's election meddling, arguing Nunes is too close to the Trump administration.

"The credibility of that committee is hurt, for all members of the committee, Democrats and Republicans, because can they now have an independent investigation on these serious allegations of Russia?" said Maryland Rep. Dutch Ruppersberger, the panel's former ranking Democrat.

So far, however, Republican leadership has shown no indications it plans to change course from having the intelligence committee alone investigate.

Nunes acknowledged Friday that the investigation is "not an easy process," but said he was hopeful the committee would move forward.

"There's politics on both sides of this and I'm trying to navigate as best as I can," he said. "I would say that what we've been very successful at is that we have people that continue to come forward to provide us information. And we want that to continue."

Some Democrats are also reluctant to see the committee turn over the investigation to an independent counsel.

"Democrats feel that if we're not engaged in this investigation, no one will be," Schiff said at a news conference Friday held minutes after Nunes'. "There are some, I'm sure in this building, who would like nothing more than this investigation to go away."

For now, the committee's work is only ramping up. Nunes at his news conference said there would be a closed session next week with FBI Director James Comey and NSA Director Adm. Mike Rogers, both of whom testified at a high-profile public hearing on Monday.

Nunes also announced former Trump campaign chairman Paul Manafort had offered to testify before the panel, while former Trump advisers Roger Stone and Carter Page told the committee that they're willing to speak about their roles in the Trump campaign.

Even ahead of Wednesday's incident, the tensions between the two intelligence committee leaders were already on display at Monday's hearing with Comey. At the hearing, Nunes pointed out that Clapper has "said publicly he's seen no evidence of collusion between the Russians and the Trump campaign," which cut directly against Schiff, who had said that there is circumstantial evidence of collusion based on former National Security Adviser Michael Flynn's communications with Russian Ambassador to the US Sergey Kislyak.

"We still really want this investigation to be non-partisan, and what the chairman did this week makes that very hard," Schiff told CNN on Friday following an impromptu meeting of committee Democrats after Nunes postponed the public hearing.

Other Democrats were harsher in their criticisms, with California Rep. Jackie Speier, an intelligence committee member, telling CNN Friday that Nunes should "absolutely" step down.

"This was all a smokescreen to cancel a public hearing," Speier said of announcing Manafort's plan to testify while putting off the public hearing. "As far as I'm concerned, that's obstruction of justice."

The Senate Intelligence Committee, meanwhile, is keeping its head down and continuing its own investigation into Russia's election meddling.

While House Democrats are calling for an independent commission, it's not clear that their party colleagues in the Senate will follow suit.

Maine Sen. Angus King, an independent who caucuses with the Democrats, raised concerns that doing so would actually set back the Russia investigation.

"The actions of the House chair (Wednesday) certainly call into question the ability of that committee to perform an independent investigation, but I don't think that applies to the Senate committee," he said.

In fact, setting up an independent commission "would take six to eight months to get where we are now in the intel committee," King said.