CalcNerd, I wouldn't go quite so far as to say it hurts, but you do make a good point. An MSEE may not pay for itself right away.
This largely depends upon what sort of Electrical Engineering endeavor one goes in to. A dual major in physics and EE might be a real asset for those designing bleeding edge devices such as low noise instrumentation amplifiers, high dynamic range radio receivers, or even analysis of synchrophasor data from the grid. An MSEE is useful when working on projects with devices such with new modulation and demodulation techniques for a next generation of cellular data service on millimeter wave bands, a new instrument for measuring flow more accurately in an industrial environment, or a better phased array radar system for a ship.
Yes, someone with a BSEE with experience is almost indistinguishable in practice from someone who has the MSEE. There is one major difference though: Recruiters and HR staff would prefer the MSEE candidate because they can verify that degree a lot easier than they can verify the experience. But like I said, right out of college, you may not see a whole lot of difference in your salary. You need to play your cards well and that will happen later.