User Verification Required for Sign-In, or
Can’t Sign In. See Preferences: Fetch -2

After much rooting around in preferences files and keychain access I determined that the cause of the problem is that Google Notifier needs access to a https keychain item for the proxy we use here. This didn’t exist for my colleague as the keychain item seems to be created by Safari when visiting a https site for the first time. If you instead use Camino then it never seems to create a https keychain item for the proxy and seems to just use the http keychain for the same proxy for https sites.

Probably Google Notifier should prompt for the https proxy username and password if it can’t find an existing keychain item.

The fix is to open Safari, visit a https site (such as https://www.google.com), enter your login details for the proxy and tell keychain to remember them. Then, restart Google Notifier, and it should ask for access to this keychain item. This has sucessfully fixed this problem for me on three separate Macs.