IFTTT – How to Use Backup Code to Access Account

It remembers your code for 30 days, but if your phone gets stolen, you just remove the "mobile application" (this means Google Authenticator) associated with your phone from the two-step settings page. This will immediately invalidate your code, and your phone browser will no longer log in*.

This is what the setting looks like in my account:

This does mean that you need to remember to remove at least two things should your phone get stolen: Your Google Authenticator application, and the application-specific password for your phone. You might also have other application-specific passwords to remove.

This also applies to any other device containing a logged in browser (like a laptop). The code will remain valid for 30 days unless you remove the Google Authenticator application in the settings. If it wasn't your phone that was stolen, you can immediately register the Google Authenticator application again and you will get new code to use.

*This is my understanding of how it works but so far as I can see this is not spelled out in Google's documentation anywhere.

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)!