This is not going to be like the other advice you get, but I've managed many projects in different organizations and I think it is sound. First and foremost, don't sound any alarms. Many organizations have common characteristics in this regard. First, they don't expect you to be on time. Sales may think you're going to launch on time, but it's in their financial interest to think so. The rest of the org probably made…
If however the project is due to slip 200%, or 400%- I guess I don't have specific advice, but that kind of project is the sort of project that can sink a company. Of course, you only really get to that point if vice-bigwigs are lying severely to the bigwigs, in which case there may be nothing a team lead can do about it.