Washington (CNN) Congressional investigators have quickly waded back into their investigations into the Trump campaign's ties to the Russians after returning from a two-week recess, with panels focused on narrower questions emerging with new actions this week.

The House and Senate intelligence committees -- whose staffers have security clearance -- have led the probes in recent months.

But this week two other panels seized the spotlight -- most significantly through Tuesday's revelation by the House oversight committee's top Republican and Democrat that former national security adviser Michael Flynn might have broken the law by not disclosing payments from foreign governments in his paperwork to renew his security clearance in 2016.

"As a former military officer, you simply cannot take money from Russia, Turkey or anybody else. And it appears as if he did take that money. It was inappropriate. And there are repercussions for the violation of law," said Rep. Jason Chaffetz, the Utah Republican who chairs the House oversight committee, in a joint news conference with the panel's top Democrat, Maryland Rep. Elijah Cummings.

It came on the heels of Sen. Lindsey Graham, R-South Carolina, announcing that a panel he chairs -- the Senate Judiciary Committee's Subcommittee on Crime and Terrorism -- would host former acting Attorney General Sally Yates to testify at a May 8 hearing on Russia's interference in the 2016 US presidential election. Yates had already been invited to testify before the House intelligence committee after May 2.

The dueling developments are both indicators of lawmakers' uneven but aggressive inquiries into Russia's meddling in the election, as those panels move in different directions and at different speeds.

The Senate intelligence committee has taken the lead in recent weeks amid infighting on the House side -- in part because Chairman Richard Burr, R-North Carolina, and top Democrat Mark Warner of Virginia appear to be working closely together.

But in recent days, some Democrats -- including Senate Minority Leader Chuck Schumer of New York -- have complained about the slow pace of the panel's investigation.

"I've made clear to leadership I have concerns about the pace," Sen. Ron Wyden, an Oregon Democrat on the intelligence committee, told CNN. "I believe you have to speed it up right now. Americans are getting most info from leaks and false tweets."

A Senate Democrat told CNN a meeting of the Senate intelligence committee on Tuesday helped clear the air among members after a round of stories criticizing the pace of the Russia investigation and staffing levels, along with some criticism directed at Burr.

The senator said that the addition of two new staffers dedicated to the investigation was a sign of goodwill for Democrats that Burr was taking their concerns seriously.

The House intelligence committee was knocked off track when Chairman Devin Nunes, R-California, defended the Trump campaign through a bizarre series of events that included a secret White House visit.

But Nunes stepped aside, and now, under Rep. Mike Conaway, a Republican working with California Democratic Rep. Adam Schiff, the committee appears to be back on track.

The committee's members met for the first time in two weeks Tuesday, and could hear from both Yates and FBI Director James Comey after May 2, though no specific date has been set.

Meanwhile, the House oversight committee has been drilling down into Flynn's work with a series of requests.

Chaffetz -- who recently announced he won't run for re-election in 2018 -- along with Cummings on Tuesday dropped the bombshell that Flynn left foreign payments off his 2016 security clearance paperwork, potentially a felony punishable by up to five years in jail.

While the committee isn't prosecuting Flynn, it has dug into his payments from Russia's state-sponsored RT TV network and a company tied to the Turkish government.

Graham, meanwhile, is playing his own role -- including launching the May 8 hearing in which both Yates and former Director of National Intelligence James Clapper are set to appear.

Through it all, the White House is largely refusing to cooperate with the investigations -- particularly into Flynn.

White House Director of Legislative Affairs Marc Short outlined in a letter to the House oversight committee how it would not complete the request from the panel, referring some requests to the Department of Defense, saying the office doesn't have custody of some of the other documents or simply stating "we are unable to accommodate" others.

The letter says one reason is that "many, if not all, documents relating to" Flynn's contacts with foreign nationals after January 20, 2017 "are likely to contain classified and/or confidential information."

White House press secretary Sean Spicer deflected questions at his briefing Tuesday about whether Flynn broke the law.

"That would be a question for him," Spicer said. "I don't know what he filled out or what he did or did not do. That all happened. He filled that form out prior to coming here. It would be up to the committee and other authorities to look at that. I don't know."

The announcement about Flynn comes a week after CNN reported that Jared Kushner, Trump's son-in-law and a senior adviser to the President, has yet to detail to the federal government all of his foreign contacts, a condition of receiving his top secret security clearance.

When Kushner first submitted his forms to the FBI, he left the section about foreign contacts blank -- despite the fact that he had met with a large number of foreign emissaries and leaders once Donald Trump became the President-elect and he became the point man for international contacts for the incoming Trump administration.