Yes you can run your camper on an extension cord from your house, but you are limited to the number of amps available for the circuit you're connected to. And that number also includes anything used inside the house.
We ran a 100 foot orange construction style extension cord from a 20 amp service to our 30 amp Springdale TT for years. It was fine for keeping the battery charged, to run a television and DVD player, even keep phones charged and such. It would run the air conditioner, but after some time, the extension cord would begin to get very very warm, an indicator it was time to shut the air conditioner off.
Eventually, I got 30 am extension cords for the camper (had 135 feet total), and the cord never got hot. But the breaker in the house did pop a few times. We learned to watch what was turned on.
When we got our new Outback (about a year ago now), I went through the effort to go ahead and install a 30 amp service in the garage. Now we have no problems with anything.
To answer your question? Yes you can run of an extension cord, but if the cord gets hot, you REALLY need to get a heavier cord! If you're going to run your camper, I strongly advise, bite the bullet and get a true 30 amp cord, long enough to reach your home to camper. You will not regret doing that.
Good luck! FYI, we sleep in the camper every night in our driveway. Hooked up the Tailgater (Dish satellite) and absolutely enjoy ourselves every day! You will too!