In my previous work, when I was under pressure (very often, because we were to few people for all the work) I used to manage the situation in the following way:

PM: It's super-important and prioritary to develop < 2 days feature >. Sales really need that feature because they cannot work without it.

Me: Ok. I'll need from them < 2-hours-to-get data > and then I can leave what I'm doing and start with the feature.

PM: *... goes to tell sales ... comes back*

PM: Well, they say they can work by doing < some not as confortable way as feature, but pretty acceptable >.

Me: Ok, then I'll continue trying to prevent the systems break down inminently.

On this work I learned a lot, but clearly, we were too few people to mantain the site, and too much lazy sales people.