For the manager of a solid company whose staff insists the sky is falling

Talk to them individually to get confirmation on what they each think is happening or will happen to the company. This will also provide an opportunity to find out if there's one particular person stirring the negativity pot, or if something non-work related is affecting their mood at the office.

Try to help with the non-work related issues privately.

Then bring the group together and have the luncheon where you list, in a very caring tone, the concerns they've brought up. Ask if there's anything else, and then address each point. You should include anecdotes for times you've dealt with similar issues, openly talk about the financial situation (if relevant), and set your direction for the future (including what role they'll each be playing in that direction).

Then go bowling afterwards - who doesn't love bowling?