If this ever happens to you, here's a solution that worked on my carpet:
1. DO NOT APPLY NAIL POLISH REMOVER. This will only smear the polish around your carpet. I would have had much less to clean up if I hadn't immediately tried polish remover.
2. Coat the stain in rubbing alcohol. If you have a spare toothbrush laying around, use it to scrub the liquid all the way down to the base of the carpet weave. If not, you can also use your finger.
3. Blot the excessive liquid up with a towel.
4. Spray the stain with Windex (I used Windex brand, so all I can do is guarantee that this type of window cleaner works), then scrub it in with the toothbrush/finger. Blot up the foam with a towel.
5. Cover the stain with hot water, and blot.
6. Alternate between Windex and hot water until the stain is out!
Tomorrow I'll be back with an awesome post about why I suddenly disappeared in the middle of Fashion Week! Something unusual but special for the music fans.
*I can only vouch for this method working on a light-colored carpet. I'd try this in a tiny little corner to be sure that this doesn't cause discoloration on your carpet!
** If you're curious, I spilled about an hour ago. My carpet had a deep purple stain. It now looks like this: