What happens if you exceed that amount?
I think you pay penalty taxes every year on the excess and any positive returns from the excess until the excess has been taken by the government or you move it out of the IRA. You have until the tax filing deadline to avoid the overcontribution penalty, so there's a window between the end of the year and filing deadlines to properly adjust the account balances. Of course, there may be other penalties involved in moving money out of a tax-favorable account early...
I also think you might be able to apply over-contributions towards the following year's IRA limits, within boundaries. I'm not sure on that, though. I generally try to make sure I'm short on Dec. 31 and make final contributions to get me up to $5500 total once I start doing my taxes (tax filing day is also the deadline to make contributions for the previous tax year) to avoid going over.
This post was edited on 5/2 at 4:45 pm