I'll echo what the previous poster said - do a bit of background research on the Manager, on the particular McKinsey office they work in, and come prepared with a few good questions. Make sure those questions are important to you; in other words, ask sincere questions where you care about the answer. If culture is important to you, ask questions about that. If the types of clients served (e.g. particular industry, Fortune 500, etc) is important, ask about that. If you care about work/life balance, inquire about that. I could go on, but I think you get the picture.
One other thing: come prepared with some form of "elevator speech" of your background, why want to be a consultant, and why McKinsey interests you. It doesn't necessarily have to be highly polished, but you should at least be ready to tell the Engagement Manager what skills you bring and why you're interested.
As an important caveat, I'm in the same boat as you: on the outside, networking to get in. I do not have a view from inside a consulting firm, but based on my experience those two things (list of questions + background material on yourself) have worked well.