Just wanted to throw my view into the ring. I actually have started my own engineering consulting company. I did this about 4 months after I graduated with an undergrad degree in Mechanical Engineering and another in Mathematics.
First off, about being PE. Don't believe that you HAVE to have a PE to work contract or consulting jobs. For MechE type stuff its not absolutely necessary. That being said, for structural stuff, it is very important. But don't think it will automatically preclude you from consulting. As long as your not signing off as a professional engineer, you can't get in trouble. You just have to make your clients aware of that.
Starting something like this is not going to be easy, and its not going to be buckets of money. Just to give you an idea, I probably make less than I would have as an entry level engineer at a large corporation. But I also have freedom. I went to traveled the world for 3 months and worked form the road. I work from home now, set my own hours, work about half the time of a 9-5, etc. I have a lot of freedom but there are also sacrifices. There can be a lot of instability. I get no benefits. I also move apartments every 4 months to keep rent down. My first few contracts were week to week and barely paid living expenses. But working hard and sticking with it can pay off. A large client (billion dollar a year corp) just gave me a long term contract and nearly doubled my pay.
I think the most important thing for starting out is networking. You will start out with zero reputation and no professional portfolio. These are HUGE obstacles. I was lucky to do some good work in school and make some excellent contacts. Talking to these people is how I got my first few contracts. Talk to everyone, tell them what your good at, schedule lunch meetings with someone 5 days a week (99% of the time they will pay because they realize you are still a poor college kid). Even offer to do work for free. For a couple weeks. If they like you, they will hire you.
One thing that is working for you is the economy. A lot of companies currently have hiring freezes. Many have the money to hire someone, but they can't commit to someone over the long term (ps the idea of entry level job security is BS). Take advantage of this by offering to work as a consultant. Make them buy you a CAD license, and computer hardware. It seems expensive in the short run, but they don't have to justify hiring a whole new team member to their boss. These kinds of gigs are GREAT for you and great for the company. You get paid more, get experience and then your not tied down at the end of the project.
Thats the short of it. Its definitely not an easy road. Signing up for a cubicle farm is far simpler and probably pays more. Send me a pm or an email and I can tell you more.