Well, time itself is a theoretical concept whether it exist, or not and that stuff just occurs before and after other stuff. If you mean that people had no sense of time by clocks, or even by weather and day-length, then our lives wouldn't be able to pass the sophistication of bacteria since, in the long run, we would have no sense of weather and seasons, possibly making it harder for us to understand how hunting works or when the best time to mate/hibernate is, and as well, we wouldn't have a good sense of how long we've been doing a certain action, so we may not know when enough is enough and it's time to back track if you've been looking for something for two days straight and can't stop. Another issue, similarly, would be the amount of time between meals as well, since, even though one may feel hunger, the mindset of how long you can put off that hunger since it's unknown how long it's been put off can also be confusing.
Basically, I think we'd be screwed. It's a deeper sense than just "we'd be late for meetings," and more " lack of proper brain functions available to fish and simple polycellular organisms with a nervous system," and our species would be at such a disadvantage that death would most likely come early.

Afterthought: Time without sleep also sucks, you know, not knowing how long you haven't slept for.