Can't sign into Gmail on iPad using 2-step verification

The Apple Mail app is not syncing with my Gmail account. Furthermore, the iPad won't download the gmail app from the app store. The app store gets stuck downloading it. After I restarted the iPad, go to the app store and find gmail, I see the "open" button, but it's non-functional. I think the problem is that my gmail password has changed. I go to Settings and search for gmail. I open up the Mail Accounts, click on Gmail, and try to "re-enter password." After entering my password, I get the 2-step verification screen, which says it has sent a notification to my iphone, ipad, and desktop. When I open the google app on my iphone, I see "403 error: We're sorry but you do not have access to his page." No notification is sent to my mac desktop or the ipad. The google app opens on the iPad, but there is no verification dialogue. Any suggestions?