What is the scheduled job linked to Scheduled SMS Reminders?
I cannot answer your direct question, but I have an alternative solution.

We are using the extension CiviRules and the extensions SMS API and Email API to achieve the same.

Then you have the possibilities to set certain triggers/events, and conditions. At the end you can set different actions, and one of them is sending sms automatically via the SMS API

We are on 4.4, so you need to try it yourself though...