In Chicago, hundreds of people gathered in Federal Plaza and marched through downtown streets to Trump Tower.
The demonstration came a day after Jeff Sessions was forced out as attorney general and Trump named Matthew Whitaker, Sessions' chief of staff, as his temporary replacement. Before joining the Trump administration in 2017, he was a vocal critic of the Mueller investigation, at one point going so far as to speculate as to how a future attorney general might "grind  [the investigation] to nearly a halt" by limiting its budget.
"The chances of Mueller being interfered with goes up dramatically" with Whitaker's appointment, he said.
"His most brazen act of obstruction has taken place in the last 24 hours", Clements said.
"If he has a close personal friendship with someone who is involved in the investigation because of his role in the Trump campaign, then that would present a recusal issue", Potter said.
The White House says the press is blowing a statement by a private citizen out of proportion, and President Trump himself insists he's never spoken with Whitaker about the probe. They also called on House and Senate committees to pursue their own investigations, and for political leaders to denounce any threat to the probe.
"There is a lot to fight against with this administration; both the president himself, but also the people he has appointed", she said. "I've had enough", Brassard said of President Trump's decision to ask for Jeff Sessions' resignation.
"The fact (Trump) passed over Rosenstein to appoint someone else who has been critical (of the probe) certainly raises concerns", King said during a stop in Oakland.
A Justice Department spokeswoman declined to comment. Sessions had endured months of public abuse from Trump, who soured on Sessions because he recused himself from oversight of the Russian Federation investigation shortly after he arrived at the Justice Department. Mueller's direct spending during that period was about $4.5 million. A dense web of regulations and professional guidelines govern how Justice Department lawyers are supposed to handle potential conflicts of interest.
Ms Pelosi added she will wait for the outcome of the special counsel investigation but noted that a call for impeachment "would have to be bipartisan, and the evidence would have to be so conclusive".
Mueller's team is paid for under a permanent fund for investigations by independent counsels that was established in 1998, which means it's not subject to Congress's routine spending debates.
Sen. Angus King said Thursday that Congress should pass legislation to protect the Mueller probe.