> anyone can do pushups if they try every day for just a few weeks
No, they can't, not even close. Fatties need to lose weight first or start with bench presses. It might not even be the matter of strength, the belly is literally in the way.
And if you're a "fatty", play to your strength - the very strong legs you have built up carrying extra weight every day.
If you do leg cardio (walking/treadmill/cycling, etc.) your leg muscle will likely never go away and you can use it to burn off as much fat as you wish. And once that is going on you can add other non-leg exercises.