Well, if you don't have the budget to design a supersonic car from scratch, why not use an old jet-fighter? First find one in a junk-yard, saw off the wings and make sure you've got a streamlined shell. Then refurbish the engine, and add steel wheels. Hey presto, a hopefully record-braking jet car.
After all, someone has already done that tedious (and expensive, what with all those wind tunnel tests) aerodynamics work for you - and proven that the engine and aircraft can reach more than Mach 1. Now for the team to raise the money they need to try things out down at Black Rock Sands...
Land speed record on a budget, anyone?