Sales guy: "They're not gonna meet the release date, and we're gonna lose the deal"
Support manager: "The customer's really angry and their data center just isn't ready to receive our stuff."
Product manager: "It's just not fast enough for this analyst testing we're doing! Don't they know we need a faster number than the competitor?!"
Most of the angst comes around a real problem: a schedule is slipping and we really are at risk of being late; or something isn't working the way it should; or it isn't fast enough yet.
What can you personally do about it?
If the answer is nothing, then you have three obligations:
1. express your concern
2. get agreement on a frequency of updates (and be reasonable about it - don't forget there has to be some work between status reports!)
3. calm down
Calling incessant meetings, sending constant emails reiterating the importance of meeting a deadline, hosting conference calls among everyone affected to discuss how it's important: none of that helps. All it does is waste time and increase everyone's anxiety level.
So let the team work.
And you go to work: if the risk is that high, it's time to put a plan B in place. Plan B should be something other than "It's gotta work". Figuring out plan B is your work, so go do it.
Worrying is helpful only as long as it's contained. Identify the risk, describe the risk, ensure the team understands the risk and the consequences of failure. Then move on to the next important steps: containing and minimizing the risk. Don't sit around and be anxious about it; it's not helpful. Be helpful.