All ridiculously expensive schools should get a bad rep for being ridiculously expensive. That being said, training physicians is expensive. State schools are subsidized by the taxpayers, so they don't have to charge as much tuition. Private schools often don't have that subsidized funding. Keep this in mind when your alumni association comes looking for you 10-20 years from now, asking you to contribute to their scholarship endowment.
To answer your question, one has to consider how badly one wants to be a physician. Would you be willing to pay $100,000 for the privilege of attending medical school? How about $1 million? I think most people would agree that the answer lies somewhere between those two values, based upon current market prices and current physician salaries. However, the answer also depends on what your options are. If GW is your one and only acceptance, you pay it up, buttercup. However, I would caution you not to spend more money than you have to. In other words, don't select GW over your state school that costs half the price if you are in the fortunate position of having the option to choose between them. In general, you should choose the cheapest school you can get into unless you have extenuating personal circumstances. I'm talking about things like being on the opposite side of the country from your spouse and children here, not things like oh, GW has PBL or P/F or XYZ other newfangled gee whiz preclinical curricular fad, and my state school doesn't, so I'm going to spend twice as much money to go to GW. Wasting money on BS like that is not a decision you'll be pleased to have made when you reach my point in life.