Trying to reproduce your problem, I enabled two-step verification for my Dropbox account and select the "text messages" option.
Installed Dropbox on one of my test VM installations (KDE MiniME 2013.02 32bit).
First time I run the client I received the error message but selected "Don't ask again".
Continuing with the configuration, I entered my credentials
Next, I got the 6-digit code on my cell phone to verify my account.
Dropbox folder created and my machine was linked to my account successfully.
I selected only one folder for sync and finished the installation.
After that, the client begun syncing my files.
I don't see any problems on my side.