I just turned on two-step identification on my Google account. It works fine on my desktop. It also works fine on my iPad with help of application-specific password.
But I have troubles with my HTC One X. Once I've turned two-step identification on, it immediately displayed a warning in notification area, that it cannot log in with Google account. Ok, when I click on it, I'm asked for a new password.
If I enter an application-specific password, I have an error - password is incorrect. If I enter my account password, it asks me to log in through browser then and redirects me into browser. Then I log in with the browser, I receive my confirmation code by sms, all works fine. Then I redirected back from the browser and have the same error!
I tried to visit https://accounts.google.com/DisplayUnlockCaptcha from my phone with no success. The only other options I saw on the Internet about my problem is to reset the phone settings. It's too hard, I'd like to try other solutions first.