I'll speak up since I'm an American living over seas and I feel like several of the comments currently ranking highly on the page either miss the point or make factually inaccurate statements. Note that if they miss the point, it's very unlikely that they choose to miss the point. More likely they have been misinformed by poorly constructed articles like this one.

I was born in the US but have been living and making most of my income over seas for five years. I'm actually relocating back to the US in two weeks (yey, welcome back :D). On the one hand I'm sad to leave the place that I currently live since, for me, it's better in nearly every way than most US cities. It's cleaner, I've lived well without a car, walked/cycled significantly more and I've visited nearly every crevice of this city and never felt unsafe due to a combination of cultural and legal differences. I pay slightly higher taxes than I would in the states. On the other hand, I'm very excited about having less paper work to do for a few years.

That's all context for my view:
For me, it's not about the amount of money I pay in taxes. I'd call myself upper middle class so far as income goes and I've not had to pay US tax for the past five years. I will have to this year because of some options that I exercises but generally I'm happy to pay US tax.

The burden, the thing that's made me consider renouncing, is the reporting. Let's start with the basics, I have to do my taxes in two places. This involves finding an accountant both in the US and over seas who is capable of doing taxes for someone who is a special type of tax resident. Every accountant will say that they are competent but I have found their claims mostly unfounded. One can pay someone who specializes but that always involves paying a significant premium.

In addition to doing taxes in two places I also have to fill out a separate form listing all assets worth > $10k and in which I have >= 50% ownership. This includes bank accounts, houses and any other investments. This is particularly onerous when one marries to a non-US resident. Suddenly the US government knows a lot about them. Do they have any bank accounts with more that $10k in them? Do they own any property? Any investments? Because if they do, by most countries standard you probably suddenly own 50% of it.

On top of all of that, as of 2015 I also have to ensure that my bank does a specific type of reporting. I'm lucky in that where I am Americans are numerous enough to make this worthwhile for the banks but this is not the case everywhere. Some banks in foreign countries have started refusing US customers.

Comparing the number of people renouncing citizenship to the total population of the US misses the point. It's better to compare against the number of americans living and working over seas. From a quick search around the internet the number of expats looks to be ~7M. It's still a very small fraction and not something that I expect law makers to pay attention to. The reason I think this comparison makes sense is because it is worthwhile to consider whether or not we want to keep connections to our diaspora. The issue from a governance perspective doesn't seem to be a loss of tax revenue but instead a non-reversible export of talent. In a flat world I have doubts about the US's ability to maintain expertise in all of the area that will fuel future economies. That being the case, I think it would be good for the US to make it simple and straightforward for Americans to go to other places where they can become experts and return home for further work.

I don't expect the US's policy to change. In fact, if the number of people renouncing continues growing more rapid I wouldn't be surprised to see the US use more aggressive rent seeking measures. This seems obvious given recent additions to the reporting requirements placed on expats and higher fees associated with renouncing.