Samsung Galaxy Tab 2 infinite login redirect with 2 step authentication
You should try to set up an "application specific" password for your tab, and enter THAT password when you enter your account details.
Now you totally avoid the second screen asking for the code.
You can create an application specific password at 
https://accounts.google.com/b/0/IssuedAuthSubTokens (at least that's the one I use)

Kind regards

joern