You shouldn't just become a project management consultant when you are unemployed. Ideally, you will have several years experience under your belt and perhaps even PMP or other certifications. You shouldn't leave a job you already have until you've given proper notice, and, until you have 6-12 months of living expenses saved up. You should also wait to leave until you have several networking contacts. You will need them when you are in a quest to find clients.
While this is the ideal situation you should have before you leave your day job to become a full time consultant, it's not always possible. If this is the case, you may be able to make things work well by starting out moonlighting as a consultant on the side.