This is word for word from http://forum.xda-developers.com/nexus-4/help/broken-digitizer-to-enable-usb-t2206706/page2 response from Dabyd64. I copied this in its entirety for reference and to have this on the Stack Exchange.
"I finally get it working by installing CWM recovery, which has ADB, and enable the adb debugging.
(if the following two commands show error "file doesn't exist", don't worry, it's ok!)
echo "persist.service.adb.enable=1" >>/system/build.prop
echo "persist.service.debuggable=1" >>/system/build.prop
echo "persist.sys.usb.config=mass_storage,adb" >>/system/build.prop"
/system/xbin/sqlite3 /data/data/com.android.providers.settings/databases/settings.db "update global set value='1' where name='adb_enabled'";
/system/xbin/sqlite3 /data/data/com.android.providers.settings/databases/settings.db "update global set value='1' where name='development_settings_enabled'";
If the sqlite3 command shows error (command not found) then your phone doesn't have sqlite3 installed.
Still, you can do it!
First extract settings.db:
adb pull /data/data/com.android.providers.settings/databases/settings.db
Copy that file to a usb drive or whatever.
Now you need linux. It's ok to use a live Ubuntu DVD, but you need to be connected to internet.
I recommend to use the 32bit version for compatibility.
Usually sqlite3 is not installed by default.
sudo apt-get install sqlite3
You will be asked for the root password!
Now we can edit the settings.db:
sudo sqlite3 /path_to_your_folder/settings.db
update global set value='1' where name='adb_enabled';
update global set value='1' where name='development_settings_enabled';
Now we have the settings.db changed and ready!
Copy that settings.db again to a pen drive or whatever, go back to windows or keep in linux if you already have a working ADB.
adb push settings.db /data/data/com.android.providers.settings/databases/
adb shell "chown system.system /data/data/com.android.providers.settings/databases/settings.db"
adb shell "chmod 644 /data/data/com.android.providers.settings/databases/settings.db"
Done! ADB should work when in starts.
I had to use "mass_storage,adb" because "mtp,adb" or just "adb" didn't work. Thought, the phone was not working in mass storage, but who cares! ADB was!"
I have used those on my Nexus 7 when I broke my digitizer and adb was turned off. It worked perfectly, should work just as well with TWRP.