Update: This is no longer relevant. Google+ allows to log in with a Google Apps account.
I use my custom domain name Google Apps account as my primary email. I still have Google account and Google profile but I am not logged into this account by default.
So when I go to http://google.com/+ I get this dreaded error message:
I found a workaround to this problem. The solution requires that a) you have a “regular” Google Account (…@gmail.com) and b) this account should be enabled the “Sign in to multiple Google Accounts” feature (thanks Paul for the tip) :
1. Go to any profile page on Google plus:
2. Click on the Account -> Switch Accounts menu:
3. Select the Google Account (not the Google Apps account) or log into your Google Account:
Bingo! Your Google plus is now working!