20 minutes a session. And do mix it up, as Chaos said. First thing in the morning, before breakfast may not be the ideal time for a lot of people to do cardio. But most people fine this is the only time they have open before work or a active, day. Would suggest something like a recumbent bike in the mornings., setting a bit high for that cardio session.
Would also suggest interval training as a faster method to burn fat and keep all that muscle that most work hard for. If doing a steady 30 minutes, or more most every day, you are approaching marathon training. If you think every serious long distance runner is in cut to ribbons shape, might look again. Or for that matter, in the best of health.
Can gain great stamina (endurance plus strength) with a well planned weight workout, with a well planned selections of exercises. Stamina training has shown to burn body fat at a very high rate, even during the day at rest. PHA/Circuit training come to mind. Don't like running of any kind, than might suggest these methods.
If you do like running, but in short durations, than it is suggested that fast sprints, run for 20 seconds with a 10 second pause and than another 20 seconds, pause, repeat. 4 to 7 cycles should fulfill all your needs for fat loss and a outstanding cardio workout. Can also do this form of training with a spinning bike, rowing machine, etc. These styles of training fall into the interval type of training. Good Luck.