What I have seen is a suggestion about squirting a LITTLE BIT of DW40 around the home button. That will likely void the warranty. Here's a "software" fix I would try first:
http://www.makeuseof.com/tag/iphone-home-button-working-fix/
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- Launch any app that came pre-installed on your device. I tried it with Notes but you can also launch Calendar, Reminders, or anything else.
- Press and hold your device’s power button for about 4 seconds, until the “Slide to power off” prompt appears.
3. Once this happens, release the power button, and then press and hold the home button instead. This will take around 6-7 seconds, but at the end the prompt will disappear, and the app will force close.
That’s it. These actions should recalibrate your home button, and if you were having problems before, you should feel a significant improvement. My iPad’s home button wasn’t driving me nuts, but it wasn’t at its best either. Doing this definitely seems to have made it more quick to respond.
The article also describes using the "assistive touch" to give you a home button the screen.
See this one too: http://howto.cnet.com/8301-11310_39-57524891-285/four-ways-to-fix-an-unresponsiv e-iphone-home-button/
Alcohol is less harmful than dw40!!
Here's another - a shot of compressed air!! Sounds like the safest.
https://discussions.apple.com/thread/3022587?start=405&tstart=0