Officials familiar with the matter describe friction on the Justice Department's fourth and fifth floors, home to the suite of offices belonging to the deputy attorney general and the attorney general, respectively, in part because of Rosenstein's handling of the Russian Federation matter.
President Donald Trump announced on Friday that he was being investigated for firing former FBI Director James Comey, and seemingly trained his guns on deputy attorney general accusing him of overseeing a "witch hunt" against him.
And, short of firing Mueller - which would be political suicide for Trump - he just has to wait and see how it plays out.
Officials who worked for President Donald Trump's transition team have been directed to preserve all records that might be relevant to the investigations into Russian interference in the 2016 campaign, according to a copy of the memo obtained by CNN.
"Americans should exercise caution before accepting as true any stories attributed to anonymous 'officials, ' particularly when they do not identify the country - let alone the branch of government - with which the alleged sources supposedly are affiliated", he wrote.
Democrats note that after the Justice Department appointed a special prosecutor to investigate the Watergate break-in during the in the 1970s, then-President Richard Nixon ordered the department to fire the special prosecutor, Archibald Cox, prompting his attorney general and deputy attorney general both to resign in what became known as the "Saturday Night Massacre". But he had said last week he felt vindicated by Comey's testimony on June 8 that he was not the subject of investigation while Comey was heading the agency. If Trump fired Rosenstein, Brand might resign because she and Rosenstein were nominated together, have a close working relationship and went through their confirmation hearings as a team.
Rosenstein, in office for less than two months, is the top Justice official overseeing the probe because Attorney General Jeff Sessions has recused himself. "However, nothing has changed". What is clear is that he could order the Justice Department to ax Mueller, which may result in Rosenstein's departure and would certainly intensify the uproar over the investigation.More news: House GOP Whip Scalise remains in critical condition, hospital says
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Rosenstein has said privately he may need to recuse himself from matters relating to the Russian Federation probe because he could become a witness in the investigation, ABC News reported on Friday.
Friday's tweets are the latest in a week of angry social media responses by the president after a report by The Washington Post that Mueller was looking into whether Trump obstructed justice.
And if Rosenstein and Brand were both out of the picture, responsibility for the investigation would fall to Dana Boente, the acting head of the department's national security division and the current USA attorney for the Eastern District of Virginia.
Boente, however, was nominated by former President Barack Obama and his US attorney's office has already been leading parts of the federal investigation. "You're going to be very disappointed when you hear the answer".
"The message the president is sending through his tweets is that he believes the rule of law doesn't apply to him and that anyone who thinks otherwise will be fired", she said.
There is also a third scenario besides dismissal and recusal.
The White House has used a memo written by Mr Rosenstein to justify Mr Trump's decision to sack Mr Comey, but that Trump action may now be part of the probe.