Google-drive – Google Keep Does not work after turning on 2-factor Authentication on Google Account

What you need to do is generate an application-specific password for each client you want to authenticate to your Google account. Then enter the application-specific password instead of your password or password + verification code.

You can generate these application-specific passwords by going to this page (use your domain name instead of example.com):

https://www.google.com/a/example.com/IssuedAuthSubTokens?hl=en&service=mail

Google provides instructions for doing this on their Sign in to mobile or desktop apps page.

Take a look at this Google Support site. Beside suggesting to send codes to your secondary phone or using a trusted computer, it also explains another way for the worst case to get access by filling out a form:

1. Sign in to your account with your username and password.
2. On the verification code challenge page, click Other ways to get a verification code?
3. Click "I no longer have access to any of these."
4. You'll then need to fill out an account recovery form to verify ownership of the account. Take time to answer each question to the best of your ability. The form was designed to ensure that no one can gain access to your account except you. Since Google doesn't collect a lot of information about you when you sign up for an account, we will ask you questions like when you created your account, what Google services you use, and who you email frequently (if you use Gmail) to make certain you are authorized to access your account.

Good luck, and if you can gain access to your account, I strongly recommend you printing backup codes and put them in a save place (or even mutliple places, you will get 10 codes)!