There is a time share condo company in Florida called Blue Green Resort, that this sounds like, or another like it. They change their numbers periodically to catch you. They tell you that you won the trip, the stay tickets to Universal, etc. but you have to spend the day listening to their spiel and pay to upgrade to one of the condo's. They sponsor a lot of the giveaways for companies so they can get your contact info. I was at Cedar Point for the 4th and they had a giveaway of a 4-Wheel ATV and my boyfriend started filling it out to enter until I saw "sponsored by Blue Green Resort" and told him to toss it.
If a legitimate job offer is coming in by phone, they will leave a message. Why wouldn't they? They certainly would not expect you to be available sitting by the phone all day in the hopes that someone might call. That would be unrealistic and would seem strange to me as a HR employee, because I would suspect that if you really wanted work you would be out looking and possibly interviewing at other establishments. If you wore not, then I would have to wonder if you were serious about being hired.