(CNN) Republicans are growing frustrated dealing with the shockwaves that reverberated through Washington as the sudden firing of FBI Director James Comey and its aftermath continue to sideline the GOP agenda on Capitol Hill.

The Comey news pushed the Senate's big health care reform effort to the back burner for several days, although GOP negotiations over how best to repeal and replace Obamacare continued behind the scenes and will again this week. Similar to the fight in the House several weeks ago, Senate Republicans remain sharply divided between the right and left flanks of their conference on issues related to Medicaid, tax credits, Obamacare regulations and more.

Many GOP members originally backed President Donald Trump's decision to can Comey because they believed the initial White House explanation that it was done at the recommendation of Deputy Attorney General Rod Rosenstein, a respected long-serving prosecutor.

But now that Trump has admitted he planned to fire Comey all along, will GOP lawmakers still support the decision or be upset about the changed reasoning? That will be a key question this week.

Trump also indicated a replacement could be nominated for the Senate-confirmable 10-year term by the end of the week. The Senate's second-ranking Republican, John Cornyn of Texas, is a leading candidate who was interviewed for the position Saturday. If he gets it, a scramble will occur in the GOP leadership ranks.

There are several possible and expected briefings this week that could dictate where the Comey and Russia stories go.

Rosenstein has agreed to brief all senators Thursday afternoon about Comey's firing, although the exact timing is not finalized, so congressional observers should be on the lookout for that event. Senate Minority Leader Chuck Schumer pressed Senate Majority Leader Mitch McConnell to invite Rosenstein, who has been at the center of the controversy after authoring a memo that recommended Comey be dismissed.

"The story coming out of the White House about why Mr. Comey was fired continues to change, and there is not good explanations for the change," Schumer said last week, explaining he also wants to have Attorney General Jeff Sessions appear in a similar briefing with all senators when he can be questioned about the matter.

Rosenstein and acting FBI Director Andrew McCabe were invited Friday to brief the Senate Judiciary Committee about the FBI's Russia investigation. In March, Comey briefed Chairman Chuck Grassley, R-Iowa, and ranking member Dianne Feinstein, D-California, about the investigation.

"We request that Mr. Rosenstein and/or Mr. McCabe, along with others who have firsthand knowledge of the briefing, provide a similar briefing for the rest of the committee," the two senators wrote in their request.

Comey, who is now a private citizen, but one who knows more than most about the Russia probe, was invited to brief the Senate intelligence committee Tuesday but turned it down for now. Committee leaders hope he will agree to appear in the near future. In the meantime, that committee has three classified sessions planned for Tuesday, Wednesday and Thursday.

Democrats plan to amplify the pressure on Trump, who threatened in a tweet last week that "Comey better hope that there are no 'tapes' of our conversations before he starts leaking to the press" -- a warning that some have interpreted to mean the President could have taped conversations with the FBI director. Trump's move prompted Democratic and some Republican lawmakers to call on Trump to turn any material over or admit it doesn't exist. The pressure began last week when Democrats from both chambers said any recordings -- if they truly exist -- should be preserved for investigators.

Senators return to work Monday afternoon and will consider nominations throughout the week to fill out several senior positions in the Trump administration, including Rachel Brand to be associate attorney general, the third-ranking position at the Justice Department.

The House returns from a one-week recess and has a busy floor schedule, with 18 bills on the calendar.

Hearings

The head of the Congressional Budget Office, Keith Hall, will testify Wednesday before the Senate Budget Committee on government reform efforts. Senators will also be interested in his work developing a final score of the House Obamacare repeal bill that the Senate is now examining.

Treasury Secretary Steve Mnuchin will testify before the Senate banking committee Thursday about domestic and international policy issues. Also on Thursday, the House Ways and Means Committee will have a closely watched event, holding its first full committee hearing on Republican efforts to overhaul the American tax system.

Finally, the Senate Foreign Relations Committee will hold a hearing on the nomination of former Republican Sen. Scott Brown to be ambassador to New Zealand, which is a long way away from his home state of Massachusetts.