You may signon to Google Drive from the app using two-step verification via the following method:

• Click the Google Drive account "Settings" pull down box in the top right of the Google Drive page. Select "Account settings". 
• Click the link "Authorising applications and sites". At this stage Google may ask you to re-enter your Google Drive account password.
• In the box under "Step 1 of 2" enter a descriptive name for the app, such as "Office2". Click "Generate password".
• The next screen contains a generated application password. This is the password that should be used in the password field when signing on to Google Drive in the app.