How do I follow up with an employer by phone?

I sent my resume to a company that I really want to work for and applied through a contact who has a lot of colleagues at the company. When I followed up with the contact, he told me to call the company and follow up and use his name. I am used to communicating these things via email, it just seems quicker and more non-intrusive.

What do I say/ask during this phone call? I’m afraid of a conversation happening like this:

“Hi my name is BluesandBlahs, I just wanted to check up on the status of my application, (contact) told me to follow up with you.”
“Yup, we got it.” (Silence) “Uh…We’ll call you if we have an opening.”
“Oh…okay…thanks!”
“Bye!”
Click
Bangs head against wall

What am I supposed to say? How do I avoid this horror-scenario of supreme awkwardness?