Simply try curl https://www.twitter.com/ to see it fails to load the ca-certificate. The problem seems to be a long-standing NSS bug: http://curl.haxx.se/mail/curlphp-2011-03/0005.html
Can't reproduce with curl 7.22.0 and NSS 3.12.11. I also upgraded to NSS 3.13.1 and it still works fine.
not sure if this is just a dupe of Bug 380119 ...
this is at least a dupe of bug 387511 ... *** This bug has been marked as a duplicate of bug 387511 ***