I can't think of any reason why SMS should fail when "email this" works -- the SMS module is just sending an email.
An easy way to do a test of the code is to edit the $carriers property in web/services/Record/SMS.php to include a fake carrier matching your library's domain -- i.e.:
'ylpl' => array('name' => ' Yorba Linda Public Library', 'domain' => 'ylpl.lib.ca.us'),
Then use the first chunk of your email address as the phone number -- i.e. 'jon'.
The SMS module doesn't currently verify that phone numbers are truly numeric, so it should send you an email if you set everything up correctly.
If you get the email but texts continue to fail, then perhaps there is some problem sending SMS messages from your library's domain. It might be worth trying to manually send an email to the same SMS address to see if that works. On the other hand, if you don't get the email, something must be broken in VuFind. I don't think this is likely… but if you find it to be the case, let me know and I'll try to help you troubleshoot.