Normally, the American Express card from JetBlue offers just 25 bonus TrueBlue points for your first purchase, 25% of what you need for a free ticket. But for a limited time (from what I've heard, just for a few weeks in July), they're doubling that bonus to 50 points, so you're half way to a free fare. After that, you get one "award dollar" for every dollar charged to the card, and 200 award dollars equals one "TrueBlue" point, of which 100 are needed for that free flight.
So doing the math, you need to spend $10,000 to get the additional 50 points you need for a free trip. But you get double points for restaurant, entertainment (sport events and such); and JetBlue purchases, so really you'll get that free ticket faster than you might think.
Apply for the card online.