In my asynchronous online class, the closest thing to group project is a Peer Review Group project.  Students are responsible for completing a peer review of thier group members' papers.  I agree that it is difficult to get everyone to participate in a timely manner.  As facilitator I try to encourage enthusiasm and participation by introducing and explaining the project details well in advance but I'm still working on ways to "tweak" my approach to this problem.

Michael, I'm required to submit grades within 48 hours.  Many of my students also wait until the very last moment to post their written assignments but for those who post ahead of time, I grade them immediately.  Essentially, I check to see if anyone has submitted thier assignment or project on daily basis.  I find that that there are at least 2 - 3 students (depending on class size) who do not wait until the last minute to submit.  Grading work as soon as their submitted helps alleviate my work load greatly.