I needed to do two things to get the MyTodoList example to work in Azure:

1) You need to install a patch to LightSwitch from Microsoft - see this thread - http://social.msdn.microsoft.com/For...f-183104678dd7

2) On the bottom of page 366 where it talks about the firewall rules it should call out that you need to check the box on the Azure DB firewall page to "Allow access by other Microsoft Services". If you don't do that you will get "errors connecting to DB" when you attempt to log into the app on Azure.

Once I got past these two issues, it worked!