Pre-interview advice?

[Ali N]

I just graduated and I am getting ready for an interview that will start my career. When I scheduled my interview, they asked me to choose a date. I chose the day after my last day at my current job. I felt it would be unprofessional for me to take time off for an interview. My family, however, is shocked that I didn't schedule the interview sooner. They keep telling me that scheduling it for a week out was a mistake, that it makes it look like I'm not interested in the position I applied for. I can't reschedule. Now I am uncomfortable with the thought that a week will go by without any communication between me and the employer I applied with. Was it a mistake to wait a week? Is there anything I can do in the meantime to communicate how interested I am?