I've just broken my touch screen, but there is an extremely important text message in my device. USB debug is disabled, and I can't enable it because touch is broken. :\ Is it possible to reach that SMS somehow? Could it be reachable via Google services somehow? The device is functional and is connected to internet.
If your device has a USB OTG port (My Xperia Z1 Compact and Nexus 7 do, and I believe most recent devices do) you may be in luck - get a USB OTG adapter (mine was from a pound shop - if your in the uk try Poundland) and a USB mouse - plug them in to your phone and you can then control it.
Its a bit of a faff at first but better than nothing.