On Monday a friend of Trump's, Newsmax CEO Chris Ruddy, claimed that Trump was "considering perhaps terminating the special counsel" - an action that would ultimately have to be made by Rosenstein.
"I think he's weighing that option", he said referring to Trump.
Rosenstein is charged with Mueller's fate because Attorney General Jeff Sessions recused himself from all matters having to do with the Trump-Russia investigation.
Yet it's a line of thinking that is making its way to the president's ears.
During later testimony before the Senate Intelligence Commitee, Comey called the president a liar, said Trump had tried to cultivate a "patronage" relationship with him, and pressured the Federal Bureau of Investigation director to shut down parts of the inquiry tied to Flynn.
Speaking from the Senate floor Tuesday, Senate Minority Leader Chuck Schumer said he was "frankly disturbed" by Trump's "hard right" supporters attempting to "discredit" Mueller and "sully his reputation". Some of Trump's allies now claim the results Mueller comes up with in the Russian Federation investigation will be tainted and biased due to Mueller's relationship with Comey and Mueller's hiring of several attorneys to help him with the investigation that the Trump boosters deem to be partisan.
Gingrich and Ruddy said it would be a "mistake" for Trump to remove Mueller, although both said they see the probe as unnecessary. Rosenstein appointed Mueller as special counsel about a week later. Doubt, however, has been cast on that explanation because of cryptic testimony from former FBI Director James Comey last week.
Barry Bennett, a GOP strategist who served as an adviser to Trump's campaign, said he believed it would be too damaging for Trump to try to remove Mueller, but that he had concerns about the appearance that the probe was being politicized.
The White House Says It Won't Answer Questions About Russia Anymore
A special counsel is now investing whether Trump's associates may have colluded with Russian Federation during the campaign. Trump has privately and publicly pinned much of the blame for his administration's woes on the communications effort.
Ruddy did not dismiss the White House communications team's words, but he did call Spicer's statement "bizarre".
Rosenstein, who appointed Mueller last month and has the authority to remove him, told a Senate Appropriations subcommittee that he saw no cause for Mueller's dismissal. The person spoke on condition of anonymity to discuss private conversations.
Adding to the atmosphere of intrigue was a tweet Monday from Trump ally Newt Gingrich saying it's "time to rethink" Mueller as special council.
In yet another blow to the president's agenda, the 9th Circuit Court of Appeals ruled against Trump's executive order limiting travel to the United States from several Muslim-majority countries. "Republicans are delusional if they think the special counsel is going to be fair".
"We also were aware of facts that I can't discuss in an open setting that would make his continued engagement in a Russia-related investigation problematic", Comey said.
"I am thrilled to have a chance to help you to live up to your campaign promises", said Commerce Secretary Wilbur Ross. Ruddy did not immediately respond to questions seeking clarification. An order from the president would not necessarily qualify, he said.
"When the day comes that our country can not rely on people to deliver the truth about whatever the subject is from positions of great authority and great reputations, like Mueller, and if we just dismiss those as not being not able to deliver us the truth about an issue we've got more problems than we think we have", Womack said.
White House spokeswoman Sarah Huckabee Sanders said via email, "Chris speaks for himself".
The White House was quick to dismiss Ruddy's comments.