So it's more like force is the AMOUNT of "pushing", regardless of the time or distance. Take for example when you press your hands together, there is a certain force, even though there is no distance, and the time has nothing to do with the force, except that it might decrease as you get tired, and will certainly vary somewhat over time.
Consider if you took some dynamic(changing over time) situation and you had a spring in between something apply force and something being moved, you could take a snapshot at any time and determine the force being applied by measuring the spring(assuming you knew it's equilibrium length and spring constant), so time has nothing to do with it.
An impulse has doesn't mean a sudden impact, and doesn't mean its "high"(especially as that is relative to what you are talking about[an elephant can probably handle much higher impulses than a mouse]). You can have an impulse of .0001N*S, taking place over an hour(theoretically), What makes it an impulse is that it is force taking place over time, not just the force we would see in a snapshot, but the measure of that "amount of pushing" for some "amount of time". The same way that acceleration would have a different meaning that acceleration for some amount of time(which is a change in velocity, [itex]/delta v[\itex]).