You've probably accidentally disabled the two-factor auth on your account. I strongly recommend checking.

My phone always asks for two-factor auth. In fact, I had to wipe my phone and re-auth, so I used one of the throw-away codes. When I re-init'd Google Auth app (which annoyingly requires disabling and reenabling two-factor auth, AND invalidates one time use keys), it immediately reprompted me to complete an oAuth cycle with the two-factor code for the core Google account on my phone.

ICS/Galaxy Nexus/etc