The rough framing should be 2-1/2 inches wider than the door itself.
That leaves room for the 3/4 inch finish frame on each side of the door, and then 1/2 inch on each side for the shims between the finish frame and the rough frame.
There are some tricks for building frames into new walls that are usually built on the floor and lifted into place.
-- Remember that there are always two studs on each side of the door for strength.
-- When building the frame on the floor, install the top and bottom piece of the wall and only the outer studs, the King Stud, for the wall -- now with a door+5-1/2 inch opening between the studs. After the wall is nailed into place, cut out the 2x4 or 2x6 that is on the floor where the door goes. Leaving it until everything is tied down will keep the door opening flat.
-- Now add the inside Jack studs, which can be nailed into the ends of the board on the floor.