I've heard this calibration method works well for people who are experiencing problems with their home button. It's worth a shot before taking it in for replacement.
EDIT: This is confirmed BS. Sorry for wasting your time and giving false hope. If a restore to factory settings doesn't fix it, take your iPhone to Apple or replace the home button with this method:
http://www.ifixit.com/Guide/Repair/Installing-iphone-4-Home-Button/3144/1
EDIT: Make sure you open a stock app in step number 1. It doesn't work if you open iFile or certain other jailbreak apps.1. Open any application
2. Press and hold the power button until the slide to shutdown swipe bar appears.
3. Release Power button
4. Press and hold Home button lightly until screen returns to icon screen
5. Enjoy your functioning home button!
EDIT: This is confirmed BS. Sorry for wasting your time and giving false hope. If a restore to factory settings doesn't fix it, take your iPhone to Apple or replace the home button with this method:
http://www.ifixit.com/Guide/Repair/Installing-iphone-4-Home-Button/3144/1