I know three or four years ago, many RFPs were indeed emergencies, requiring really quick responses. Planners often didn't get the green light from their higher-ups until the last possible minute, due to the unpredictability of the economy. It forced a lot of us to scramble, which meant our suppliers had to scramble to get us what we needed, ASAP.
Today, I don't think every RFP really IS an emergency - I think it's a lack of understanding on the planner's part about what really goes into a proposal. It's just a template, after all, right?! Well, sort of. Many suppliers use templates, but they still have to infuse them with creative solutions to meet your group's special needs, figure out all the moving pieces to assure a good fit, and determine special concessions to make the proposal attractive without breaking the bank. It takes a lot more than 24 hours to put together a strong proposal, and that's if they have nothing else going on and can drop everything to focus on it (riiiight, because we're all just waiting at our desk for emergency projects to drop).
So planners, do you really need your proposals in 24 hours, or is it just a habit to ask for this turnaround time? Can you spare a couple extra days? The more time you allow, the more organized you seem, and the better (and more customized) your proposal results will be. If you DO need every RFP response in 24 hours every time, perhaps there's some better system you can implement - I'm sure you don't need the constant stress, either.
If ALL you need at this stage is a quick response with just rates/dates/space, be sure to note that you don't need a full proposal.
Your suppliers will thank you!