Thank you for the reply.
My host is GoDaddy. Can you give me some more information on by the "PHP/Curl install"? I would think they would have the necessary settings, but maybe it's something on my end I need to upgrade? I can't be the only person who is hosted by GoDaddy and is communicating with Google.
The only solutions I've found were to turn off the certificate check, which sounds like the wrong answer. (like fixing the check engine light by putting a sticker over it)
I realize that it's a bit outside the context of your plug-in (that it's doing what it's supposed to, as you mention), but I appreciate any help. Thanks!
(I'm continuing to dig myself)