While it may sound counter-intuitive, ask for help from the busiest people you know if you want things done quickly. Busy people know how to time box projects. So, with short deadlines, you can be sure that the project will be done efficiently. On the other hand, when people have fewer things competing for their attention, it's easier to procrastinate.
By asking my busiest friends for help first, I also think twice about whether I actually need help or whether it'll be easier to just do something myself. When I first started doing this, I felt like I should be asking for help from people who have more time to spread things out more evenly. But, as long as you ask whether your request is reasonable, your busy friends should give you an honest assessment of whether they can help.