(CNN) With James Comey's testimony in the rear view mirror, Congress looks toward trying to move forward this week on one of the more traditional aspects of their job -- budget hearings.

But with Attorney General Jeff Sessions facing questions about another possible meeting with Sergey Kislyak , and Secretary of State Rex Tillerson having to field questions about President Donald Trump's statements on Qatar, these hearings could be anything but mundane.

And it all starts Tuesday morning, when Sessions and Tillerson will both be on the Hill. Sessions said over the weekend he would testify before the Senate intelligence committee, thought it was not clear as of Sunday night if he would testify in public or private.

Tillerson will appear before the Senate foreign relations committee, and his House testimony will be Wednesday afternoon. Deputy Attorney General Rod Rosenstein is scheduled to testify before the appropriation committees for the Justice Department while Sessions testifies before the intelligence committee.

Health care:

Five weeks after the House passed their version of the health care bill, folks in the Senate say there are still a lot of obstacles to bringing conservatives and centrists together.

Negotiations continue. Majority Leader Mitch McConnell wants to have a bill they can take to the congressional budget office for a score next week, though Majority Whip John Cornyn doesn't expect a Senate vote until after the July 4 recess.

More budget hearings:

On Monday and Tuesday, Defense Secretary James Mattis will also testify before committees related to funding. He'll appear before, respectively, the House armed services committee on Monday evening and the Senate armed services committee Tuesday morning on his department's budget.

Treasury Secretary Steve Mnuchin will do the same before the Senate budget committee Tuesday at 10 a.m. ET.

Thursday, Health and Human Services Secretary Tom Price's turn in the witness seat before the Senate appropriations committee, and on Friday, Acting FBI Director Andrew McCabe will return to discuss the bureau's budget before House appropriations. Expect a lot of questions to not be about the budget.

Notable meetings:

We are expecting that special counsel Robert Mueller will be meeting with Senate intelligence committee chairman Richard Burr and ranking member Mark Warner at some point this week. And Trump adviser Jared Kushner will also be meeting with intelligence committee staffers this week, though we don't have specifics on a day or location as of this writing.

And both the Senate and House committees will hold closed meetings this week -- the Senate on Tuesday and Thursday and the House on Wednesday and Thursday.

Sanctions:

The Senate may vote next week on additional sanctions on Russia, following months of angst among senators on both sides of the aisle who've wanted harsher US action against Moscow for meddling in last year's presidential election, exact timing to be determined.

On Monday, the Senate will vote on a motion to move forward on the Iran sanctions bill, which is what the Russia sanctions amendment would be attached to. An agreement could be possible early next week.

Everything else: Health care, veterans affairs

The House will also vote on legislation next week beefing up accountability measures at the Veterans Department following some high-profile scandals. The Senate already passed the bill, and then it will go the President's desk for his signature.

On Monday, 11 days after the start of Hurricane season, the Senate homeland security committee will meet to consider the nomination of Brock Long to become the FEMA administrator.

And, if you have designs of owning a self-driving car in the future, you'll want to hear what the Senate commerce committee has to say on Wednesday. Per the advisory, "the hearing will explore automated vehicle technology and hurdles for testing and deployment in the United States. The hearing will also examine state and federal roles to ensure safety while promoting innovation and American competitiveness."