Here is a simple solution to fix a slow or unresponsive home button. (re-calibrate)
Try this first before resorting to replacement of the Home Button.
I have had this solution get a totally unresponsive Home Button to work again many times. It works on all iPhones, I have not tested on but I am sure it that it should also work on iPod touch and iPads. It is commonly caused by a software glitch or your iDevice has alot of installed apps.
I sometimes like to compare it to a Disk Defragment in Windows. Though it's an Apple Operating System.
1. Open any application. For this example I will use Settings.
2. Hold down Power Button till display shows the Shutdown screen. Like image below.
3. Now let go of Power Button and then start to continuously hold down the Home Button until the "Slide to Power Off" screen disappears. Be patient, eventually it will return to the Home Screen. It may even take between 1 - 2 minutes.
That's it. Now test by opening any application and then pressing the Home Button to return to Home Screen.
If you need something more visual to follow try this YouTube video.
(Images courtesy of Google Images)