Contacts, contacts, contacts. Your contacts don't get you a job. They get your resume put in front of the person who hires. It put your resume on top of the stack of 200 that the hiring person is looking at.
Here is what I would ask my contact::
"What's your input about getting hired at (where they work)?"
"I'm really interested in working at (where they work). Would you be willing to give my resume to the (Nurse Manager, DON, Personnel Director, etc)?"