Absolutely. And that's when the PCs really have to manage their resources properly because they won't get the rest breaks they otherwise might, won't have as many chances to study/pray for spells, won't get their overnight heal rate as often, etc. And some adventures should totally be like this; where the choice as to whether to plow ahead or to stop and rest has potentially very serious consequences either way*.
Some adventures, but not all. Each adventure really should have its own pacing - sometimes the party might think they're on a clock when they're actually not; other times they might not know of a deadline until it's too late; another adventure might have a well-known and hard deadline, while a fourth doesn't have any time limit at all.
* - note this still doesn't completely work in a 4e-style situation where resources (other than dailies) are not really diminished that much as you go along - you've always got your at-wills, you've got your encounter powers to pull out once per fight no matter how many fights you get into, and so on.
Lanefan
See, I don't really agree with deceiving my players deliberately, so if there's a clock, they'll know of its existence, and if there's not, they won't. The DM creates and controls the world, he should at least have the general decency to make his creation not deliberately deceive the players.
But then again, I've clashed over DMing styles before with most of the truly old-school DMs on this board. It just seems like most of their DMing techniques work best when the party has a pile of extra character sheets they can use once their current character dies, and "roleplaying" consists of "I'm a dwarf! I like ale!"
For some odd reason most of the player demands (super consistent worlds, tons of rules for building monsters, known and highly predictable values for all events) seem to be based on the concept that the DM is a backstabbing jerk who will deceive them at every opportunity and builds things simply to screw with their heads.
But that's probably a different topic.