Diet and cardio (walking, jogging, swimming, etc.) will cause you to lose weight.
Sit ups and push ups will just help build muscle. You will just end up building muscle on top of fat.
If you are pressed for time stick with water, vegetables and protiens. Then exercise (not work out, huge diff) and you will start losing weight.
Once you get down to what you should be for your age and height, start working on muscle.