If you've just installed Evercontact for Google Apps & see this message, then please do the following as seen in the screenshots below.

1) Go to your Google Admin Console & click on Security:

(sometimes you will not see Security in this menu, and you'll notice that there's an option at the bottom "more controls", click there and add security)

2) Finally, the API must be enabled. If it's not here's the quick process to get it set up.

a) In Security, click API reference:

b) Check Enable API access.  Then, click Save changes:

c) Lastly, go back to the original web page where you had the "You're Almost There" message and refresh that page.  If for any reason that doesn't take you to your Evercontact Team Settings, please contacts us at support@evercontact.com so we can resolve the issue.