If you're not excused over the phone, you must appear on the date specified on your summons. Appear in court as directed. Again state your reason for wanting a deferral when the opportunity arises for jurors to make such a request. Be cooperative and polite no matter what happens. If you are excused, expect to receive another jury summons when your stated availability date comes up.
Courts are notorious for turning down requests to be excused.
What you think is a good reason may not be good enough in the eyes of the judge, so be realistic. Unless your excuse is found to be valid, chances are your request will be turned down. There are a few legitimate reasons for being disqualified completely from jury duty. Check with your county or state court system for a list of these. States and counties have individual laws regarding penalties for not appearing in court if you have been sent a jury summons.