I don't know how much of this will be public to start with, but I don't foresee a deadline being imposed from the WH.
Lots of ways this could lay. Sessions could write Rosenstein and demand assurance that Mueller is NOT working on any investigation other than "the campaign," other than whatever Sessions has recused from.
Sekulow, Cobb and Dowd can do the same thing, to Rosenstein and to Mueller.
Congress has oversight over the DOJ, and should be upset if a Special Counsel usurped the role of the DOJ, or stripped sessions of a power that Sessions had not relinquished. I doubt Congress does anything though, Congress all but endorsed Comey usurping the role of prosecutor.
Sekulow Cobb and Dowd can also take to the press with their arguments. OpEds, appearances on news programs. Ask the people to complain to Rosenstein, flood his inbox, swamp him, bury him with attention. Turn on the spotlight.
Yes, but with all due respect, what of those options produces a situation that terminates the effort? If whatever Trump or Sekulow or any of these guys does just rattles the Press or writes this guy a letter or any of those other things what’s to prevent this from going on for 5 years?
The concern that I have is more spiritual and tactical....at what point does Trump say “I have the right to fire the special counsel if I wish. Instead I’m going to give him an amount of time to complete this investigation to show his results. Hit it or quit it. This shows that he is in charge. If he never does something that shows that he is in charge ....he will never be in charge. That’s the simplistic tactic I’m sort of floating here. Drop the hammer.