There is a myth out there propagated by jokers who want to sell people products and programs that have you only working out for 60 minutes total for a week and that overtraining is a real risk. That all you need is 20 minutes a day, three times a week, anything more is overtraining. BS. Overtraining is really f-ing hard to achieve for most people. The real risk people actually run into is under-recovery. To properly recover you must have nutrition and rest.
Nutrition: If you eat properly, taking in enough protein and carbs to match your physical exertion levels you are good on nutrition.
Rest: If you sleep properly, getting at least 7.5 hours, your rest should be hitting a proper target. But this is the more likely area you are lacking. Get your sleep!
Anybody just starting out with lifting weights along with some cardio should be advised to take it easy at the beginning. Starting with 3 sessions per week of 40-60 minutes would be an okay starting point. One session of 20 minutes is not enough, in any universe. I would also argue that 3 sessions of 20 minutes per week will not be enough for very long, but starting with something is better than nothing. To get results over time you will need to put the time in.
Assuming you have been doing some regimen for several months and beyond, the "overtraining" syndrome becomes less and less likely as your body will adapt. If you work out smart and don't kill your joints with a bunch of silly accessory lifts and follow the Stimulate, Don't Annihilate principles you should be fine as far as working out smart. The body can take a lot more punishment that most of us actually give it. If you work a desk job that has you doing jack squat for 40+ hours per week, I would suggest your body is starving for more stimulation.
There are only so many days you can lift "heavy" or put on a lot of volume but there is plenty left in the tank to fit in energy work, crossfit style workouts and boring old cardio. Elite athletes get into the double digits on hours per week spent training, including all forms. I am not suggesting you hit this type of threshold unless it can be a full-time gig where everything in your life revolves around training, then eating, then sleeping. Rinse and repeat this trifecta multiple times per day.
I do think a reasonable goal per week is 300 minutes, which equates to 5 hours for the math majors out there. Break this down any way you want but 300 is a realistic goal. This could be 4 gym sessions of 50 minutes, and add in 3 cardio sessions of just over 30 minutes and you hit your 300.
If right now you are quite a ways from 300 you can begin week to week by adding a few minutes per session, or the better route is to add in some extra shorter sessions. 20 minute sessions are fine, but not if you only do them 3 times per week and nothing else. Actual weight training sessions where building muscle is a goal should be 30 minutes minimum to get a bang for you buck. But if you want to do several cardio sessions at only 20 minutes per because you don't want to blow your brains out, I get it. Do as much cardio as you possibly can outside, that will help a lot!
At the end of the day your body can probably be pushed much harder than you currently push it. If you are properly taking care of yourself it will be quite a challenge to reach an overtrained state. Don't be afraid to push it.