Hi Stev,
No, the Sparkfun example doesn't use 2-step, but if the Google account is set up to use it, the Galileo won't be allowed in with just the standard password.
If you haven't heard about it before now, you are probably not using it on your account.
I guess you have already found this, but for others, here is a bit of explanation on the 2-step verification stuff from Google: http://www.google.com/landing/2step/
For applications like the Galileo or 3rd party mobile apps, they have a feature called application specific passwords: Sign in using App Passwords - Accounts Help
It seems like you might be experiencing something else, maybe a spelling mistake in the password or similar, and when the Galileo tries again and again, Google sees that as suspicious activity.
I might give it a try and see I can get it working, though I do for sure use the 2-step verification on my Google account.
/Thomas