(CNN) President Donald Trump's son-in-law, Jared Kushner, has volunteered to speak to the Senate Intelligence Committee as part of its investigation into Russian meddling in the US election, a White House spokesman said Monday, kicking off a critical week for Congress on the issue.

"Throughout the campaign and transition, Jared Kushner served as the official primary point of contact with foreign governments and officials," the White House spokesman told CNN in a statement. "Given this role, he has volunteered to speak with Chairman Burr's Committee, but has not yet received confirmation."

The Senate committee sought Kushner, who is a key adviser to the President, as part of its investigation, two sources told CNN Monday. The timing is still being determined, a Senate aide said.

The New York Times first reported the Senate committee's request, because of his role in arranging meetings between campaign advisers and Russian ambassador to the US Sergey Kislyak, along with other foreign leaders.

Lawmakers investigating Russia's role head into the week with the prospect that the House investigation could struggle to stay away from drama and a continued push by Trump's supporters to shift the focus from Russia to leaks in the intelligence community.

House investigators set the stage last week with a blockbuster revelation last Monday that FBI Director James Comey is investigating ties between Trump's top campaign aides and Russian officials along with calls from some Democrats Friday for Rep. Devin Nunes of California to step down as chairman of the House Intelligence Committee.

Senate investigators, meanwhile, have stuck to a slow and steady pace beginning to interview witnesses in private and scheduling their first public hearing -- set for Thursday -- with none of the high-profile figures that punctuated the House's first public hearing on the matter.

Meanwhile, the stakes couldn't be higher for the White House, as Trump comes off a shocking loss on health care and attempts to find his footing for his policy agenda moving forward.

Can the House Russia investigation survive?

One week ago, the House Intelligence Committee provided the stage for Comey's stunning revelation that federal investigators are conducting a criminal probe into whether top aides for the sitting US president coordinated political attacks with Russian officials in their bid to win the White House last year.

That statement set off an immediate firestorm, punctuated in part by Trump tweeting commentary from the official White House account while the hearing was still going on and White House Press Secretary Sean Spicer offering the shocking -- and inaccurate claim that former Trump campaign chairman Paul Manafort played a "very limited role" last year.

But two days later Nunes effectively revived Trump's wiretap claims by reporting that Trump's own communications may have been picked up in "incidental" collections by domestic spies . Nunes then went to Trump directly with his findings -- but never told Democrats on his own committee.

Trump said he felt "somewhat" vindicated by Nunes' findings.

The fiasco set off a firestorm of allegations from top Democrats that Nunes was colluding with the White House -- something Nunes has denied. He also later apologized to Democratic members of the committee.

Democrats were up in arms Friday as well after they said Nunes arbitrarily canceled a public hearing scheduled for this Tuesday, and said he would replace it with a closed-door briefing from Comey and NSA Director Mike Rogers. (Nunes said he was only delaying their second public hearing.)

But Nunes also canceled the closed briefing with Comey and Rogers, Monday, saying that they would try to reschedule.

"Director Comey and Adm. Rogers could not come in tomorrow as we'd hoped, so the Committee will continue to try to schedule a time when both of them can meet with us in closed session," Nunes spokesman Jack Langer said Monday.

By the end of the week, a Democratic source on the House Intelligence Committee was convinced that Nunes was trying to "suicide bomb" their investigation.

Now House investigators head into another week jam-packed with evidence collection and a top-tier private briefing -- and the ongoing tug of war for the focus of the House investigation.

"We can't have a credible investigation if one of the members, indeed the chairman, takes only information he has seen to the White House and doesn't share it with his own committee," ranking Democratic member Adam Schiff said Sunday on CBS "Face the Nation," showing the weekend did little cool relations between Nunes and the Democrats on the committee.

Can Senate investigators make headway with less drama?

While the House Intelligence Committee is pulling apart at the seams, Senate investigators appear to be on solid ground. Two members on that investigation -- Sen. James Lankford, an Oklahoma Republican, and Sen. Angus King, a Maine independent who caucuses with the Democrats -- said as much at a joint news conference last week.

One thing that appears to be helping Senate Intelligence Committee has been a low-key approach so far, interviewing witnesses quietly in private. And Senate Intelligence Chairman Richard Burr, a North Carolina Republican, has shied away from the cameras for the past two months, leaving his House counterparts to dominate the airwaves.

Some of that will change Thursday, when the Senate Intelligence Committee hosts its first public hearing in its Russia investigation. But instead of two high-profile witnesses at the center of the current investigation (like Comey and Rogers), the two confirmed witnesses are cybersecurity experts who are likely to offer a more circumspect view.

All of this does not mean that Senate Republicans and Democrats don't face the same partisan pressures that House investigators are facing. (Indeed, Thursday's hearing will be a good gauge of where most senators are based on the questions they ask.) But the Senate has so far ducked the chaos unearthed in the House last week.

The Ranking Democrat on the Senate Committee, Mark Warner of Virginia, told NBC's "Meet the Press" Sunday that Nunes' moves as "fairly mystifying if not outrageous" and said he's trying to keep the Senate's investigation as open to the public as possible.

"We're going to continue to do as much as we can in public," he said, adding later, "There's a lot more smoke."

Can Nunes and other Trump allies push the focus away from Russia to leaks?

It was striking when Nunes reported last Wednesday he had discovered evidence that Trump transition aides -- and possibly Trump himself -- were picked up by domestic spies monitoring foreign agents, but the communications had nothing to do with Russia.

But it was a good reminder that the House's investigation is not limited solely to Russian interference in the US elections. Instead Nunes followed through on a promise that he would try to out the sources who provided information to reporters.

As the stream of stories about Russian contacts with top Trump aides has grown into a river, the President has consistently focused not on the reporting from inside the intelligence world, but instead on who is providing the information to reporters.

But efforts by Republican members of the House Intelligence Committee to focus their questions on leaks and "unmasking" of US citizens in intelligence reports fell largely flat in last Monday's hearing, paling to the news that the FBI was investigating top campaign aides to the president.

In that context, Nunes delayed a second public hearing originally scheduled for Tuesday, which could have easily turned into a repeat of Monday's stunning marathon. Instead, Comey and Rogers will return for a private briefing.

Nunes initially promised that Comey and Rogers would meet privately with lawmakers instead, but he canceled that meeting as well.

Pushing back is Schiff, who has argued that evidence he has seen of possible collusion between the Trump campaign and Russian officials would be strong enough to present to a grand jury.

Enough to get a special commission?

Intentionally or not, Nunes gave House Democrats plenty of ammo last week to call on Ryan to create a special commission to investigate Russia's interference in the 2016 elections. And Nunes' own work on the Trump transition team became more of a liability after last week.

Nunes only added fuel to the fire Monday, when he told CNN's Jake Tapper that he met with his intel source last Tuesday on White House grounds. Rep. Jim Himes, a Democrat on the House Intelligence Committee, called Nunes' decision to meet there "loopy" and "bizarre."

Top Democrats immediately took advantage of the opening. House Minority Leader Nancy Pelosi of California called Nunes a "stooge" for Trump, citing his work on Trump's transition team. And Schiff was given the microphone for the Democrats' weekly rebuttal to Trump, to make the case for an independent commission.

"Congress should establish an independent commission that has the staff, resources and single-minded focus necessary to investigate this matter," Schiff said. "Most important, as the events of this week demonstrate, an independent commission will be able to conduct its work insulated from any political interference."

But a simple fact of life remains: House Democrats are almost powerless in the minority. They cannot force Ryan to do anything, they can only attempt to make it incredibly uncomfortable to continue supporting Nunes.

Republicans appeared ready to dismiss the need for an independent commission Sunday.

"I heard my friend from California (Schiff) mention an independent commission," House Intelligence Committee member Trey Gowdy, a South Carolina Republican, told CBS "Face the Nation." "Thank goodness we have one. It's called the FBI."

Manafort, Stone, Page and ... Flynn?

In quick succession Friday, lawyers for three of the top targets in the FBI's probe — Paul Manafort , Roger Stone and Carter Page -- said their clients would gladly testify before lawmakers . And Manafort's own communications team has been actively emailing reporters, offering up counterpoints to intelligence sources, noting that it was not strange for US operatives to find work from Russian oligarchs from 2005-2014 during a time in which two US administrations were attempting to open up relations with Putin and Russia.