The way you phrase this makes it sound like you have to work harder to burn more fat as you get more fit. This is not true. Say your cardio workout consists of running at N% of your max heart rate for 1 hr, covering a distance D. The more fit you become, the greater distance you will cover running at the same N% of your max heart rate. Since the number of calories you burn is proportional to the distance you run (work done), as you get fitter you will burn more calories without needing to exert additional effort. Cardio is a good way to lose weight, esp in combination w/strength training.
Anaerobic threshold. It's the point where your body produces more lactate than it can burn, so excess lactate accumulates. (When I say point, this is generally expressed as both a heart rate and also a speed, but you usually pace your workouts based on HR.)
working out at a fixed % of AT will make sure you cross over into anaerobic everytime. That is true. but at the same time, you will have to do more and more work to get to that point, and I think people underestimate how much that is (and thus get frustrated with cardio and blame exercise in general, poor genetics etc.). Purely as a time measurement, the amount invested just doesn't make sense vs. lifting. why not just cut to the chase and start with anaerobic exercise, since it looks like we agree that that's what burns the fat?
edit: I should also reiterate, as many have below, you ALSO get the cardio benefit from lifting.
Let's say your anaerobic threshold is 190bpm, and you are working out at 155bpm. That means you can never go over your AT by definition, since you are always changing your pace to keep your HR fixed at 155. Essentially the longer you work out the slower you go, so that your heart rate never increases.
In order to burn the same amount of fat you will constantly have to be doing more exercise, maybe that clarifies?