Getting "Sorry there has been an unknown error" error

Getting "Sorry there has been an unknown error" error when entering username and password in on the Account Settings form and clicking on the Check Account Details button here: admin/config/services/constant_contact/setup.

We had been running beta3 and it was reported users were getting a "Sorry, there was a problem, please ensure your details are valid and try again" when trying to submit a Constant Contact registration form. I upgraded to the latest version, 3.6, but that didn't help. I re-entered our credentials per above.

I started to dig and I found the http_send function where the cURL code connects to the Constant Contact server. I added the following settings so I could better debug:

curl_setopt($ch, CURLOPT_STDERR, $f = fopen('/path/to/a/directory/you/have/access/to/curl.log', "w+"));
curl_setopt($ch, CURLOPT_VERBOSE, TRUE);

I then clicked on the Check Account Details button again and got the following error written to the curl.log:

* About to connect() to api.constantcontact.com port 443 (#0)
*   Trying 208.75.122.62... * connected
* Connected to api.constantcontact.com (208.75.122.62) port 443 (#0)
* Initializing NSS with certpath: sql:/etc/pki/nssdb
* Unable to initialize NSS database
* Initializing NSS with certpath: none
* Unable to initialize NSS
* NSS error -5925
* Closing connection #0
* Problem with the SSL CA cert (path? access rights?)

I see that the module has the following SSL setting:

curl_setopt($ch, CURLOPT_SSL_VERIFYPEER, 0);

Not sure what to make of this. Is this an error on our side? On their side?