Another reply to the "We don't have any openings" right now response is the Upgrade Your Staff Technique. While most managers scramble to find a new person when they lose a valuable staff member, very few think about upgrading their staff when they are at full employment. Here is how it works:
"Since you are fully staffed, now might be a good time to consider upgrading your staff. When the economy is growing, it will likely become harder and harder to find competent people to add to your staff. You might consider this an excellent time to make plans to upgrade your staff. Would it be correct to say that the most valuable member of your staff isn't necessarily the most skilled, but the one with the greatest passion for their work?"
(Wait for "Yes" or "Probably")
"Well, Mr./Ms. Manager, it's that same passion for excellence, that same attitude of giving my all that I would bring to you and your department. I'd like the chance to meet with you and prove that I have what it takes to become a key member of your department. I am available the week of March 16th, with Tuesday and Wednesday wide open. Which day would work better for you?"
Again, it doesn't always work. But it sure gets them thinking beyond the "no openings" objection. And don't be surprised if they think about it and give you a shot. This technique plays on the vanity of the manager and their desire to be out in front of the game. Who could blame them for planning in advance? Certainly not you or I.