A good number of the states require that you have some residency training in order to obtain a license to practice in the respective state. In addition, without any residency training, you will not be able to sit for any of the board certification exams, which is required by most of the hospitals for any privileges, whether it is surgical or non surgical. At this point, most students (if not all) are expected to do a residency training. The only exception would be the Canadian students who are returning back to their own Province to practice Podiatry.
The following link will provide you with info on each particular state for licensing. The majority of states require at least a year but as all residencies are moving to 2 or 3 years (majority will be 3 year surgical), expect the requirements to change. Also, keep in mind that in order to sit for rearfoot surgical boards, you must have a 3 year residency (as of 2007). And as dpmgrad pointed out, it would be difficult to find employment or get privileges at a hospital with minimal training.
You can't get a license to practice in most states (~46) without CPME approved postgraduate training. The only CPME approved postgraduate training are residencies, either 2 or 3 years.