rotating tires = 4 at a time?
Anyway, for what it's worth,
I find it much much easier to carry a can of fix-a-flat or other inflation type thing. (Bike pump is currently in the car.)
And a tire-patch kit... the one with the long poker thing, the glue, and the sticky hunks of rubber. Pump tire, wet tire, locate hole. Move car slightly forward if necessary, locate hole. Put rubber thingy on needle thingy. Jab into hole, push hard to insert the rubber thinging in so that it's barely hanging out. Remove pointy thingy. Inflate tire with pump. Done.
Quicker than jacking and replacing a tire.