Oh yeah, also to comment on the urgency thing: I don't mind the ticking timer, especially when their is a hud on screen that already takes away from full emersion.
For those games that do try and sink you into an experience by removing the hud, they can just give you something visual in the environment, like water rising or an object coming closer to you, to tell time.
So an avalanche is coming, you have 3 minutes to evac, BUT you don't want that ticker on screen. Well first you make sure that the avalanche is visible. Then you give the player a set amount of time, like someone says over intercom, "Oh crap! An avalanche is coming!! You have approximately 3 minutes to evac!!! Get that computer chip and get out of there!!!!". So now you have a mental time frame, you can see the avalanche slowly creepy towards you, you have an objective to complete within that time frame, and now you should feel some urgency.
As for a bomb exploding, i'd just have a guy yelling over intercom, "you have 30 secs"....."you have 10 secs". Or in the environment, place screens in the map every so often that'll give allow you to see the time that's left. Of course that need to be in the right context, like a command station that has a self-destruct button and screens that displayed the self-destruct time but yeah....you get my point hopefully
So yeah thats my solution Making it an environmental timer, rather than a obvious clock above your head would deal with Jeff's problem i think.