When you are working on a non-existent budget you need to be able to cut some of the "above the line" crew positions.
A financed film is a bee hive of various people trying to work together. Every small aspect of the film has an individual taking responsibility for it, and this method both increases efficiency and also spreads out the creative responsibility. When you are beginning production on an ultra low budget independent digital video feature you do not have the cash to arrange an army of people to put together your film. From the list of standard positions you are going to have to weed out some and know what can be handled by other people.
Know Who You Need
Before you try to cut positions out you have to know which ones need to stay. The producer is the commander in the nervous center of the film and they are needed to coordinate the overall production. The director is the prime creative position and makes all the decisions about the film product itself. The director of photography runs the camera and makes all the decisions as to what images are actually captured for the film, and the sound director does a comparative job with sound. Along with these you are going to need someone for light and microphone operation during production, especially since the director of photography will be behind the camera and the sound director will be listening and changing technical settings. On some productions you are going to need someone to consistently work on make-up and hair, but you will know ahead of time if this is something your film requires.
Script Supervisor and Unit Production Manager
The first thing that often needs to go are the more technical positions like the script supervisor and unit production manager. These are very important positions, especially on more complicated projects, but if you really need to narrow it down their tasks can be easily distributed between the producer and director. This will take even more organization, which should be addressed during pre-production.
All assistants need to be eliminated from the staff. This is a lot harder than it sounds because often times the assistant to an above the line position is the acting hand for that position. Even if you choose not to get rid of the unit production manager there is no reason to allow an assistant. Likewise, all second unit work needs to be done by the primary director.
The art department as a whole is one of the most important parts of a film crew. If you are working on a very low budget the director may have to take the position of art director, and they may have to work alone. If you have enough work to be done for an entire art department then you are already going to have to spend large sums of money simply on materials. This is the same for people working on special effects, set construction, location scouting, model or vehicle construction, and so on.
Spreading Out the Work
From here on out think about dividing all tasks up between seven or eight main people. If you have less then that you are going to have to crunch even further, but also remember that many of the common film positions only exist to help organize massive studio projects. Since yours is smaller and simpler you need fewer hands on it.