WASHINGTON — (CNN) Some Senate investigators are chafing at the pace of their investigation into Russia’s interference in the 2016 election and possible coordination with the campaign of President Donald Trump, three months after the Senate intelligence committee formally opened its probe.

A source with knowledge of private conversations told CNN that Sen. Mark Warner, the lead Democrat on the Senate investigation, is “very frustrated at the pace of the committee’s investigation.”

It took Senate intelligence Chairman Richard Burr, a North Carolina Republican, and Warner nearly two months to negotiate with the intelligence community the ability to get key, sensitive information. And they finally got what both men have said is an “unprecedented level of access.”

But the frustrations are far from boiling over into the dysfunction, which almost derailed the House Intelligence Committee’s investigation a month ago.

“I wish there were a way that it could go even more quickly but I think it’s important that we be thorough,” said Sen. Susan Collins, a Maine Republican on the Senate intelligence committee. “And I was very happy we had the open hearing to hear from Russia experts, which put in context the efforts of Russia over the ages. The two leaders of the committee work extremely well together and we get a briefing all the time from them every week on where we are.”

Senate investigators have gained access to the intelligence typically reserved for the small “Gang of Eight” — an exclusive group of House and Senate leaders with top-level intelligence clearance, which include leadership as well as the chairmen and ranking members of each chamber’s intelligence committee. And staff have been talking with the analysts.

Senate investigators, a source said, are a long way from bringing in high-profile targets like former Trump campaign chairman Paul Manafort, former Trump national security adviser Michael Flynn, former Trump campaign adviser Roger Stone and former Trump foreign policy aide Carter Page.

But Warner has previously noted that he doesn’t want to rush interviews with key witnesses before understanding critical details.

In the Capitol, the House Russia investigation has drawn the most attention by far — beginning with FBI Director James Comey’s stunning revelation last month that the FBI has been investigating Trump aides since last July, through to House intelligence Chairman Devin Nunes’ surprise recusal from the investigation as he became the subject of a House ethics investigation stemming from his secret trip to the White House in March.

The consternation comes as lawmakers return from their two-week break, which saw much of the heated debate about the investigations die down, capped by Nunes’ recusal just hours before House lawmakers left town.

The gears have been turning slowly behind the scenes in the Capitol, but mounting anger in public outside Washington has been clear in town hall confrontations and polling.

An NBC/Wall Street Journal poll released Monday found that 73% of respondents want an independent commission instead of Congress to investigate Russia’s interference. Only 16% of respondents said they preferred Congress.

The Senate Intelligence Committee has hosted a pair of public hearings in its investigation so far. The House invited former acting Attorney General Sally Yates, former Director of National Intelligence James Clapper and former CIA Director John Brennan for its second public hearing May 2, following weeks of partisan wrangling over the hearing in private.

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