I have the similar problem as you today and I think I solved it.
First I am assuming that you have a google map api key already. I think what you need to do is to to go API Console – Google Code and click on API access
on the left. You can see your api key and just below the key, Referers:
shows your allowed referers. What you need to do is click Edit allowed referers...
and then add
localhost/*
to allowed referers.
I am using a MAMP to host my html, and I monitor the request my browser sent to google for api and I get this header:
showing Referer as localhost/*
It takes several minutes for Google to process after you changed your Referer but it works fine for me afterwords.