I have used Spirit several times over the last 6 months and I worried about the exact same thing. After my initial flight, I realized that a lot of the passengers were carrying on bags that exceeded those dimensions and I didn't notice any bags being charged. Here is the list of Spirit flights that I have been on since the beginning of the year.
Denver--->Detroit (2X)
Detroit--->Denver
Denver--->Fort Lauderdale
Fort Lauderdale--->Denver
On my first flight with Spirit I decided to bring a larger bag and pay the checked bag fee in advance and it didn't cost too much. After that flight, I have used a mid sized backpack that is a larger dimension than listed and didn't have any issues. If you bringing something a little larger than I think you will be fine but if you bring something too big and it won't fit under the seat then they will have to charge you for it. Based on my travel, I haven't seen them push the issue too hard (unlike Allegiant Air) but I am waiting for that to change at some point in the near future.
I have also noticed that with most of the planes, they have reduced the distance between rows of seats, so you will be pretty uncomfortable if you are tall. It is definitely worth paying the extra $10 to get an emergency exit row, if available.
