Following these steps I also go the problem where I was continually prompted for my username/password.

Eventually I got it working by doing the following:

1) Click on "My Computer"
2) Click on "Map Network Drive"
3) Click on "Connect using a different username"
Enter your me username and password, then click 'OK'
4) Select the Drive Letter you want to use.
5) Enter the path \\idisk.me.com\dave.johnston
6) Click Finish