But within the party, there was more evidence bubbling of calls to start hearings - especially from some of the Democrats running for President in 2020.
In his statement, Mueller made clear that "there was insufficient evidence to charge a broader conspiracy" involving the Trump Campaign and Russia - but when it came to matters related to obstruction of justice, Mueller repeatedly said he could offer no such judgment.
"As set forth in our report, after that investigation, if we had confidence that the President clearly did not commit a crime, we would have said that," Mueller told reporters, as he repeatedly said he was constrained by Justice Department policy which does not allow criminal charges to be brought against a sitting President.
"Charging the President with a crime was therefore not an option we could consider," Mueller said.
There are 36 paragraphs in the statement by Mueller - seven of them went over that same subject, as Mueller repeatedly noted, "a President cannot be charged with a federal crime while he is in office."
Mueller said the only other option available is in the Constitution, a process which does not involve the criminal justice system.
That would be impeachment.
Other than Rep. Justin Amash (R-MI), no Republicans in Congress have called for additional hearings about the Russia probe - other than to 'investigate the investigators' for potential bias against the President.
"Democrats should immediately end their Russian hoax obsession," said Rep. Mike Rogers (R-AL).
"It is now time for us to move on as a nation," said Rep. Chris Stewart (R-UT).
"Robert Mueller did not find that the president obstructed justice. Case closed," said Rep. Andy Biggs (R-AZ), as a number of GOP lawmakers criticized Democrats for entertaining the idea of an impeachment proceeding.
Even if Democrats launch a formal impeachment inquiry - or continue with investigations before a variety of committees, it's not clear if Mueller will testify in public, as he made very clear he doesn't want to be in that position.
"The report is my testimony," Mueller said. "I would not provide information beyond that which is already public in any appearance before Congress."
But some in both parties said he should appear.
"Mr. Mueller’s statement today is a case study in pettifoggery, and reinforces my position that he should be compelled to testify before Congress," said Rep. Tom McClintock (R-CA).
"We look forward to Mueller's testimony before Congress," said Rep. Adam Schiff (D-CA), who chairs the House Intelligence Committee.
"I believe that the American people deserve to hear testimony from the Special Counsel about his report and the report's conclusions," said House Majority Leader Steny Hoyer (D-MD).
Whether it results in an impeachment inquiry - that remains uncertain.
"The Congress will continue to investigate and legislate to protect our elections and secure our democracy," said Speaker Pelosi.