Both points are notable. Sessions was once considered one of Trump's closest advisers and enjoyed access few others had. Now he is left to endure regular public criticism by his boss.
Trump's suggestion, too, that his top law enforcement official investigate a former political rival is astounding, and even his allies have said in the past that such a move would be unheard of in the United States. Trump, after the election, had backed away from the idea of possibly prosecuting Hillary Clinton.
Sessions's tight relationship with Trump and the White House has unravelled since he recused himself in March from the Russia probe. The President had privately complained about that decision for weeks, and in an interview with the New York Times last week he said he would not have appointed Sessions as attorney-general had he known that Sessions would do such a thing.
After Sessions recused himself, he passed on the responsibility to Deputy Attorney-General Rod Rosenstein, who then appointed Mueller as special counsel overseeing the Russia investigation.
Trump could order Rosenstein - and then Associate Attorney General Rachel Brand - to fire Mueller. If they quit instead of doing so, he could appoint an acting attorney general who would. Trump could also appoint an acting attorney general with them in place - effectively passing over Rosenstein and Brand - and order that person to remove the special counsel.
Trump's authority to jump Rosenstein and Brand, though, is murky. The Justice Department has issued opinions in the past saying that such a move is and isn't permissible. And his pick for an acting attorney-general would have to have Senate confirmation and be serving elsewhere in the government or have worked in the Justice Department for 90 days within the past 365 and be at a certain senior pay level.
Another scenario is that Trump could make a recess appointment, said Steve Vladeck, a professor at the University of Texas School of Law. Under that plan, Trump could choose an attorney-general during the August recess who would serve until the end of the next Senate session, which could be early January 2019. That person would have the same authority as someone who is confirmed by the Senate, Vladeck said.
Among the names being floated as possible Sessions replacements are Senator Ted Cruz and former New York Mayor Rudolph Giuliani, according to people familiar with the conversations.
Giuliani dismissed a report mentioning his name as a possible attorney-general and told CNN that Sessions "made the right decision under the rules of the Justice Department" to recuse himself. He did not return a message seeking comment.
In a statement, Cruz said he was "deeply gratified that we have a principled conservative like Jeff Sessions serving as Attorney-General. The stories being reported in the media tonight are false. My focus is and will remain on fighting every day to defend 28 million Texans in the US Senate."
But not all in Trump's orbit share the view that Sessions' days are numbered.
Anthony Scaramucci, the new White House communications director, told CNN that Trump and Sessions "need to sit down face-to-face and have a reconciliation and a discussion of the future".
Former House Speaker Newt Gingrich, a vigorous Trump ally, said in an interview that he and Trump had talked about Sessions and that Trump had indicated "he was very unhappy both with the recusal and the fact that Jeff didn't talk to him beforehand". But Gingrich said he would "strongly oppose" the firing of Sessions, because "I think his base likes Sessions."
