What is it like competing for such RFPs? Sounds like it's not for the faint of heart. Have you managed to make a pleasant/sustainable career out of this sort of work?
Competing is a pain in the ass, since at the end of the day lowest bidder basically always wins. So it really ends up a race to the bottom and I've seen more than one contract to go bidders offering to do projects basically at a loss.
There is another way however. Many places have a lower limit, where projects under that don't have to go out for bids. Find out what that limit is and keep your project under that limit. This does require you to get to know people in decision making positions, developing an understanding of what problems they face and sell proposals directly to them.
I don't compete for such RFPs (I'm actually kind of on the other side of the table at the moment :) ).
However, I have friends whose companies do, and yes, they've made a sustainable career out of this sort of work.
The key "secret" is that, by the time the RFP comes out... it's almost always too late. It's much better to have built rapport with the organization, know its needs... and at least over here, the RFP will be written with one or several products or companies in mind.
There are several very good answers here (dagw's point of finding the lower limit is a great one), and I've also seen other good posts here on HN, I'll see if I can dig some up.
What is it like competing for such RFPs? Sounds like it's not for the faint of heart. Have you managed to make a pleasant/sustainable career out of this sort of work?