With the Model S you can; depending on how you drive, the 60 kWh pack would be tight, but the 85 kWh pack should handle you no problem (going on your second 250 mile requirement). Those same numbers aren't out for the Model X, but as I said, they are the same battery packs, and the total efficiency will be in the same ballpark.
Also, note that just because one particular non-extended-range electric vehicle does not meet your particular driving requirements does not mean it is a useless endeavour, or even that it will fail in market at all. There are plenty of other people out there that don't drive 300 miles a day (I for one wouldn't want to); the base Model S would do all the driving I need fine, except when I go home for the holidays. Even then, the 85 kWh battery pack would handle that no problem. If you're going on a really long trip, say, once a year, you could always just rent.