I'm looking for a cheap portable electric pressure washer.  The
feature it must have is the ability to store water within the unit (I
don't have a hose).

If you want to have a water store tank that will supply you with water
you will need a trailer or skid mount unit that you can mount on the
pick up truck. If the unit puts out 3 GPM than in order to use it for
let's say 30 min  you will need at least a 90 gallon size water tank.
There is many websites where you can find this kind of equipment, just
search under trailer mounted pressure washers.
This is not an inexpensive unit but is the only way to accomodate your need.