Last night my Home button stopped working on my iPhone. I found this fix in the Apple Forums which should at least keep my phone functional until I can either get it repaired or replaced.
Go to Settings > General> Accessibility > Physical & Motor > AssistiveTouch ON
Once you turn the AssistiveTouch option to ON, a small black screen will appear and you should click the Home option in that area. It will place a white ghost button on your iPhone. You can move it around so it’s where you’d like it. When you need to press your Home button, you’ll press this ghost button instead and it’ll open up that black screen again and then the new Home button on your screen. Basically, it’s a few more steps each time, but it’s better than pressing the original Home button a zillion times and it not doing anything.