push ups or any resistance training wont help move them alone.
you could try putting on some muscle and the increase in your metabolism may shift the fat. if not you'll have built a decent chest and then strip the fat by cutting.
or try shifting around your cardio, do HIIT, resistance cardio, circuit training.
it tends to be that the place you most want to lose the fat is the last place it will shift from. i have a problem with ass fat, a big one. im thin enough on top and all the weight moves from there quite easily. the ass is less happy to oblige, so i got down to a decent body fat% and have started to bulk a bit; in the process of this the ass is back but i am definitely better built not and when i start to cut the fat again ill be more proportioned and better equiped to burn it (more muscle=more kcals burned).
this is the most horrible part of getting rid of unwanted body fat; you can work your arse off and still get no where. experiment with cardio and mix it up; but id suggest you start looking at a 6 top 12 month plan and accept that long term goals dont always fit in with what you want right now. i can put up with a bigger backside knowing in 12 months im going to look nice and lean!