I'm a graduate student who still leaves homework for the last moment sometimes. This mantra of going hard early can also be applied to a few of my assignments and academic projects.
Properly designed academia would probably remove procrastination from K to PhD.
The deadline is just so the setter has a schedule to assess it, and the next one will be coming at some point in the future.
With work it's usually all coming now. If you're not doing task a, you could be doing task b, c, d or e instead. Of course good planning and management will mean time is organised between all the tasks to get them done one at a time (or as close to) and it's not a daunting pressure, but I find there's always a sense that there's lots to do.
In the cases I've had where there doesn't seem like a lot to do, that's when I tend to procrastinate with what I'm meant to be doing, looking at this and that other interesting thing we could be doing.
[Edit] Also, money always helps ;)