Currently Being ModeratedFeb 21, 2014 9:02 PM (in response to GLaura)
Did you get this to work? To find where you need to put in the password, you can go to Mail > Accounts... and System Preferences will open. Select your gmail account and it will prompt you for a password. Copy and paste the password from google's 2-step process to the prompt field.
For me, I also had a problem where some mail would get stuck in the outbox. To fix this problem (at least for now), I also made a separate app-specific passcode for the Outgoing mail server. You can access this in Mail by going to Mail > Preferences then the Accounts tab, then select your gmail account on the left. Click on the dropdown menu by "Outgoing Mail Server (SMTP)" and select "Edit SMTP Server List..." In what pops up, make sure to select the right gmail account, then make sure "Authentication" is set to "Password." The "User Name" field should be your gmail address, and the password field should be the app-specific password that google supplies (that you must paste in).