So hard to say. You could start with 4 aircraft on a single route. You could lease MD80s and have your fleet in place for about $300,000 in downpayments (assuming you got your lessor to cover configuration costs). You contract out for all the ground handling and maintenance, set up two stations, hire about 50 to 75 people, secure gate and counter space at two airports, cut deals with Travelocity and others. You need to buy, or apply for, an operating certificate from the DOT, and get your operation blessed by the FAA. The regulatory side can go quickly (if you buy an existing certificate and airline manuals), or slowly (up to a year).
I'm going to say (really guess) that you need $1,000,000 cash to start up a bare-bones 4 aircraft operation. Probably need another $1,500,000 (cash or line of credit) to cover operating losses until you start to fill the planes. Break even load factor will probably be in the 65-75% range, so the route(s) you pick would be critical. Of course, if there is any such under-served route, any existing airline could step in and fill the need in a heartbeat. If you became a threat to another carrier, you could get snuffed out pretty quickly.
Airlines on a shoestring are really hard to pull off because the industry is so competitive and efficient right now. That's why JetBlue is where it is. They opened up on day one with a very efficient operation, wads of cash, and a brand new fleet. All the compromises you make to minimize the start-up costs (old planes, contracted services) make you a less efficient operation.
[Edited 2004-03-27 17:21:40]