Space Politics has an article on Newt Gingrich and space prizes. There are a number of good comments you should look over, and judge for yourself. I'll just repeat my comments below (see the link above for the context) since they contain some links that I think are worth following up.
If I remember correctly, in “A Case For Mars”, Zubrin talked about a human Mars Prize along the lines of this $20B prize from this article, as far as I can tell from the short bit on it. This was supposed to have come from discussions with Gingrich. In the one in “A Case for Mars” there was a really big prize for an actual human Mars mission, but there were a number of incremental steps, made of smaller prizes, that led to the final goal, as some folks here are recommending. As you might expect, the steps followed the “Mars Direct” idea pretty closely.
I agree with the posters that suggest that prizes will tend to work better for projects that have more immediate follow-on economic usefulness. Perhaps that would be things like tugs, solar sails, space access demos, refueling, better instruments or better satellite components. A reasonable substitute for general commercial usefulness would be usefulness to government agencies that could then buy the new service (eg: NASA moon mission components).
Of course this is all fantasy when we’re wondering whether or not Centennial Challenges will get $4M this year.
Here are some Gingrich items on this subject, just FYI (since the referenced article was a bit brief on the subject). Like Richardson, at least he knows what the X PRIZE is.
Youtube - Gingrich on NASA and prizes
Examples of Prizes Incentivizing Behavior - April 2007 - Gingrich
National Prizes Foster Innovative Solutions - 2002 - Gingrich
Kerry vs. Gingrich debate
and one from Jeff himself: Space Review article from Jeff Foust
Ray (Space Prizes blog)
Update: Also see the post and comments at Transterrestrial Musings.
Here's an excerpt from an old article with a section on a "Mars Prize" from Reason.com:
The Mars Prize. Zubrin tried selling this idea during a dinner with then-House Speaker Newt Gingrich, who got so enthusiastic that the meal lasted for four hours. But Gingrich never followed through on the proposal, which calls for Congress to promise $20 billion to the first explorers who reach Mars and return. In case that prize isn't enough to interest entrepreneurs in such a risky all-or-nothing venture, Zubrin also envisions offering smaller bonuses for achieving technical milestones along the way, like sending the equipment for making fuel to Mars.
Prizes have been used in the past to spur public-private ventures in exploration. Fifteenth-century Spanish and Portuguese rulers offered financial inducements to captains who ventured down the African coast and across the Atlantic. In the 19th century, the British Parliament offered cash awards for reaching the North Pole and for venturing westward into the Arctic ice: a prize of [sterling]5,000 for reaching 110 degrees west, double that for reaching 130 degrees, and triple that for 150 degrees.