Asked if his House Oversight Committee - which pursued Hillary Clinton on a number of fronts in recent years - should get involved in any probe of Flynn, panel chairman Rep. Jason Chaffetz (R-UT) said, no.
"It's taking care of itself at this point," Chaffetz told reporters several times.
"Would that have been your attitude if Clinton was elected?" one reporter asked as Chaffetz hopped on an elevator in the Capitol.
Other Republicans were also cool to the idea of pursuing Flynn.
"I don't know enough details right now to know whether we should have a hearing on this," said Sen. David Perdue (R-GA).
Others - including President Trump - were worried about what had been leaked about Flynn.
"This stuff was learned through press reports - and that's concerning, because it means there's also leaks from the Intelligence Community," said Sen. Marco Rubio (R-FL), who told reporters that he was not ready to call for any testimony from Flynn as yet.
At the White House, officials pointed the finger of blame squarely at Flynn, while acknowledging that Mr. Trump had been told several weeks ago that there were questions regarding one of his top aides.
"The level of trust between the President and Gen. Flynn eroded to a point where he felt he had to make a change," said Press Secretary Sean Spicer.
"The President decided to ask for his resignation; and he got it," Spicer added.