Barr announced that Berman was "stepping down":
“I am pleased to announce that President Trump intends to nominate Jay Clayton, currently the Chairman of the Securities and Exchange Commission, to serve as the next United States Attorney for the Southern District of New York.
... I thank Geoffrey Berman, who is stepping down after two-and-a-half years of service as United States Attorney for the Southern District of New York. ... I wish him well in the future.”
Pretty typical Barr stuff. He doesn't waste time and energy in a public debate.
Berman, on the other hand, is attempting to push back, claiming that he won't step down until Clayton is confirmed:
Berman was appointed by the US District Court for the SDNY under a rather special (and sloppily written) legal provision--28 USC 546(d):
If an appointment expires under subsection (c)(2), the district court for such district may appoint a United States attorney to serve until the vacancy is filled. The order of appointment by the court shall be filed with the clerk of the court.
Berman's seems to be claiming that the appointment by the Judicial Branch in this special circumstance somehow immunizes him going forward from the normal operations of the DoJ. That's an argument he'll certainly lose, based not only on Constitutional principles but also on 28 USC 509, which states that:
“All functions of other officers of the Department of Justice and all functions of agencies and employees of the Department of Justice are vested in the Attorney General.”
I take that to mean that, once appointed in those circumstances by the Court, the USA is subject to the AG. And can also be fired by the President.
That's also the idea as expressed in 28 CFR 0.5(a):
§ 0.5 Attorney General.
The Attorney General shall:
(a) Supervise and direct the administration and operation of the Department of Justice, including the offices of U.S. Attorneys and U.S. Marshals, which are within the Department of Justice.
Brett Tolman addresses all this, point also to 28 USC 541(c), which allows the President to fire US Attorneys irrespective of other provisions of law. He adds:
[28 USC 546(d)] does nothing to modify the President’s authority as it is a temporary executive position not a judicial position. It is still an executive branch position despite judges inserting the temp. And you obviously know who heads the executive branch.
The real point is that Barr is inexorably extending his control over DoJ and he's not about to let anyone stand in his way. He has the authority and he'll use it. Period.
UPDATE 1: It was never an issue whether Barr would back down. Barr has asked Trump to fire Berman, and Trump has done so. In a letter to Berman today, Barr stated in part:
Unfortunately, with your statement of last night, you have chosen public spectacle over public service. Because you have declared that you have no intention of resigning, I have asked the President to remove you as of today, and he has done so. By operation of law, the Deputy United States Attorney, Audrey Strauss, will become the Acting United States Attorney, and I anticipate that she will serve in that capacity until a permanent successor is in place. See 28 U.S.C. 541(c).
To the extent that your statement reflects a misunderstanding concerning how you may be displaced, it is well-established that a court-appointed U.S. Attorney is subject to removal by the President. See United States v. Solomon, 216 F. Supp. 835, 843 (S.D.N.Y. 1963) (recognizing that the “President may, at any time, remove the judicially appointed United States Attorney”); see also United States v. Hilario, 218 F.3d 19, 27 (1st Cir. 2000) (same). Indeed, the court’s appointment power has been upheld only because the Executive retains the authority to supervise and remove the officer.
UPDATE 2: Sundance notes that Barr has a previously scheduled interview tomorrow with Maria Bartiromo and speculates that the Berman firing today may have been timed to help put across a narrative that Barr has had in the works for a while. We shall see. It's true enough that Barr doesn't engage in interviews without having some point that he wants to get across.