The next best way to handle the "Send me your resume stall"—especially if you are not located near the company—is to offer to e-mail your resume directly.
Persistence always scores more points than mere experience.
Tell the person you will e-mail your resume and call back within a half hour. By doing this, you accomplish two goals. First, you immediately overcome the initial stall. Second, you put information in their hands that can take you to the next step in the process: setting up the interview. Delivery is nearly instantaneous, so you can then carry your dialogue to the next level (i.e., setting up the interview). Wait exactly 30 minutes, then call back to follow up on your e-mailed resume. You have now overcome the staff and can set up the initial interview.