I can't disagree with the above advice, but I'll add something that hasn't been mentioned.

What makes whiskers really tough to cut is sebaceous oil. This oil is more heavily produced in the triangle formed by the top of your nose and the base of your chin (which is a big part of why the mustache and goatee area are so hard to shave). The longer you go without shaving, the more oil gets into the whiskers, and it collects dust, and hardens into a scale. Now, IF you do a very good prep and break down the oil and scrub it off, then the whiskers can absorb the soapy lather and get really soft.

Of course, you still need a sharp razor, as well.

Also, short stubble tends to stick out more at a right angle to the skin, whereas long growth tends to lay over some. This increases the amount of the whisker you have to cut, since you are slicing through it on a long angle.