Excess fertilizer kills plants because the salt content in the soil prevents the roots from taking up water like they normally could.  As long as there is still a fairly high salt content in the soil, the grass will not regrow.  In a heavy spill, nothing will grow, sometimes for a few years.

The solution is to decrease the salt content in the soil, usually through a process called leaching.  This is done by dissolving the salt in water and having it leach (drain) deeper down into the soil profile.  After enough of the salt has been leached, plants can grow in that area again, but it can take time.  You can speed the process up by repeated watering, saturating the soil so that the excess water drains down into the profile.  Another option for smaller areas is to dig out the soil and replace it with fresh soil.  Usually if you dig down a few inches, that should be enough but it will depend on how much fertilizer was spilled and how long ago the spill occurred. The greater amount of fertilizer and the longer its been there will mean that you will need to remove soil, deeper down. 

If you notice that you spilled some fertilizer it is a good idea to try to get it cleaned up right away.  Use a broom an dust pan, a shop vacuum or what ever else you can do so that it does not stay on the soil to cause a problem.