You, and lots of others, including me and a few of my employees using my Google Apps domain. I followed Googles recommendation to sign up for 2-step verification and then followed authentication problems exactly like you're describing. Fortunately, there's a link for that: Recently enabled 2 Step Verification? Having trouble with your password? - Gmail Help
Originally Posted by rstark18
Even a few of us that hadn't signed up had issues, but then did and followed the instructions, and not an issue since. Yeah, I wish Google would let us know this stuff, but they don't, not even for paid accounts like mine. BTW, following the instructions stuck - for each of us, but I sure was ticked off until I found the link...
Happy New Year!