I've been unable to log on using my mobile (without wifi). I input the code sent and the page simply refreshes itself (Java disabled). If Java is enabled, the page refreshes itself every second to load the countdown timer. Clicking to choose other method yields no results at all.
I've been hearing about problems with mobiles and the new two factor authentication. Seems to be a fairly widespread issue although I might be exaggerating based on limited information.
My advice is to just turn off two factor if it is important that you have mobile access, but if security matters more than access to you, keep it on.
Success! First attempt to log in using Android browser was successful with Java enabled. The countdown timer also behaved as it should rather than refreshing the page every second. As for Hoy's suggestion above I didn't have any luck with that as the "data saving" function in chrome was already disabled. I haven't changed anything on my end so whatever you guys did worked. Thanks much.