They seemed to have their own culture and priorities that I was not a part of. I knew my own project inside and out, of course. I studied about the departments they led, and talked to people who had experiences with them about their decision-making style and motivations. I had remarkable cooperation and more assistance than I would have dreamed. Many of these VPs told me later that my enthusiasm and knowledge of my objectives was the key to overriding their other priorities and getting me what I needed.
Many management schools teach deadlines and accountabilities.
Those things are very important, but trying to force a deadline or accountability usually does more harm than good. It is very important to outline what you need. You must have a thorough understanding of the specific tasks that need to be done by specific dates to make the project work. However, you have much more success at getting deadlines and accountabilities that stick when people at least feel like they have some say in setting them for themselves. Outline what is needed, and ASK for that person's help and cooperation.