Lies and office politics

I've commented a few times here that my new job is very different from what I have been used to. My new job is mostly about people and meeting with them to get things done. Yesterday was a very frustrating day. I understand that I have to deal with office politics and the way things go in my office, but the good news is I have the opportunity to work with five separate groups that all work together for the betterment of the company rather than each individual organization. That has made it easier on my, but it also let my guard down. I was working with another team that is a part of my overall organization and when they told me they had done all the preliminary work on a project we were working on together I believed them. That lasted right up until I had called around and sent emails getting the project going and crowing about what an amazing success it portended. Then the time came to actually put it into practice and it turns out not only did the other group not follow through with what they said they had, but they didn't even know what follow through meant in the way of work! They agreed they had done all the work and didn't even know what work needed doing. Some stuff I am willing to write off as people not willing to expose their ignorance or not understanding things completely, but outright lying to my face is more than I am willing to work with. Now I get to play office politics with this group that lies to me. They now have gone from a week's worth of effort to get their project going to involvement of a month or more and they expect me to drop everything for them.
I find that outright lying to me to be the worst. I try to give people the benefit of the doubt, but I become very frustrated and I am unwilling to give my best efforts to those people as well. I suppose we'll see more how it pans out on Monday when they expect the month's effort rather than ask for it.