You should have very few problems in finding somebody to supervise you if your academic qualifications are up to scratch. Projects with research grants have been peer reviewed, based not only on their scientific/academic merit but also on whether or not they are acheivable by a PhD student within 3 years. If you're funding a project yourseslf then less scrutiny will have been applied (it could be that only you and your supervisor think it's a good idea). Canvas as much opinion on the research project you choose as you can before parting with your cash.