Remember, these folks don't always have the information you need themselves. They may have to ask others for it. Limit your request to what you need. If you do need everything, you can get it - but explain why. Finally, give them all the time you can.
Emergencies come up.
Consultant support people have dealt with emergencies before and will again. But for each real emergency, they also see ten consultants claiming to have an emergency - usually because they, the consultants, procrastinated. This rarely happens. By itself this probably won't change things, but it is an important preliminary for the next steps. If you sign one, take it seriously.