One problem: This Senate will not confirm a replacement for Rosenstein.
If that's true, then the Senate might not today, when it doesn't have access to The Memo, but it might when The Memo is finally released and it becomes clear Rosenstein was a ringleader and HAS to be kicked out of office. With Sessions recusing himself on so much, there's no question he needs a deputy. It's just that he needs one who is on Trump's side, not on the side of the now out-of-office conspirators who had dreams of becoming lifetime dictators.
One problem: This Senate will not confirm a replacement for Rosenstein.
Recess appointment.
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One problem: This Senate will not confirm a replacement for Rosenstein.
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Keep firing\prosecuting (though, you’d need to START the latter first) until they relent.
If Trump replaces him with someone who has already been confirmed for another position in the executive branch, then they can serve for months in an “acting” capacity even if the Senate refuses to confirm them.