I learned all the time limits by sitting and waiting after I received these quests. Some of the time limits are really short, but knowing them at least would give you a chance to plan ahead when you see one:
"Help Defend" settlement quests only give you a 15-hour window (15 hours on Pip-Boy clock) for you to complete. That's barely enough time for you to do a fast-travel if you happen to be far away. So these quests are the most urgent.
Kidnapping quests give you a 2-day window to complete. If there are two stages to the quest (i.e. talk to the settler, then rescue the kidnapped victim), then you get a 2-day window for each.
"Raiders trouble...","Ghouls problem...", and "Greenskins" quests give you much more time: a 15-day window. If there are two stages, you get 15 days for each. These are the only ones you can put off. Still, 15 days on the Pip-Boy is just 18 hours real time.