Cutting the passenger load by 80% doesn't necessarily mean that you can cut the overall vehicle weight by 80%. It's like those homebuilt aircraft designers who want to build a scale replica of a WWII fighter. Some things, like the pilot, don't scale well.

It's certainly possible to build a small 1 or 2 seat car that would weigh far less than even the current generation subcompacts. My first car was a 1974 Honda Civic. It had a curb weight of about 1600 pounds and an engine that put out roughly 50-60 HP, if memory serves. It was a fun car that was very maneuverable (and that maneuverabily saved me from a potentially fatal accident on more than one occassion).

Steel in auto construction is well understood. Both the design programs and assembly lines are already set up to handle steel construction. Changing to another material like aluminum could reduce the vehicle's weight but it could require some expensive rework of the assembly line, such as the ability of industrial robots to perform spot welding on steel but not on aluminum. That alone limits your choice of materials if the goal is to develop an affordable small car. If affordability isn't an issue (and it has to be), then you could go with aerospace materials like carbon fiber and really cut the weight. However, the cost of using such materials would be too high for most people to justifiy on fuel savings.

You can cut a lot of weight at the margins in a really small car and the savings can add up fairly quickly. For example, a full 5 gallon gas tank might weigh about 35 pounds (30 pounds for the gas at 6 pounds per gallon and 5 pounds for the tank) compared to a full 15 gallon tank that might weigh 100-105 pounds (90 pounds for the gas and 10-15 pounds for the tank). If the car gets really good mileage, say 60 MPG, then a 5 gallon tank should be plenty. You can use smaller wheels, brakes, and tires for another savings of perhaps 60-90 pounds. You'd save with fewer seats, smaller (but not thinner) windows, lighter engine and transmission, etc.

However, there are other things that you can't reduce very much if at all. Your controls like the steering wheel, brakes, switches, etc. are likely to be just as big in the supercompact as in the subcompact. Headlights, brake lights, and other critical safety items will probably have to be just as big and heavy, perhaps due to federal requirements.

Just as a SWAG, I think you could use essentially conventional construction techniques (lower design and production costs) to build a practical 2 seat car that would meet federal guidelines (emissions controls, seat belts, crumple zones, air bags, etc.) and would weigh under 1000 pounds. With good streamlining, low rolling resistance, and an engine of perhaps a 40 HP engine, the vehicle shouldn't have any trouble getting 50-60+ MPG with acceptable acceleration. Done right, it could be a fun car to drive.

The question is how many of them could you realistically expect to sell. Getting any new car design into production typically takes years and several hundred million dollars. You have to have an expected market big enough to justify that kind of investment. There are already really small cars on the market that get good gas mileage. They aren't selling very well. Using numbers pulled from my anal data store, if it cost $300 million to go through the full R&D cycle and set up an assemply line for this car and if you could realistically expect to sell 100,000 a year for several years before needing to update it, then the R&D costs alone would probably exceed $600 per car. Add in the cost of materials and labor and you'll have a hard time making a profit for less than $10,000 per car.