I feel like the OP should have specified whether they meant period or just for a trip out of the bag with no laundry/shopping trips/etc. I can live out of a single bag indefinitely if I have regular access to laundry and can replenish my toiletries. As can most of us, I'd think. At least as long as you are sticking to a single climate.

Actually living out of a carry on with no laundry or purchase of new toiletries? That's probably more along the lines of a week in summer or 5 days in winter. Longer if I didn't care about being smelly.