Mounting an USB wireless adapter to a Nexus 4
There is a very good chance that you may not have a driver problem.

There is a very important detail everyone seemed to miss about using network connections via USB: they must be plugged in before the phone is powered on! The phone must also have Wifi and Data turned off, and potentially Airplane Mode! All before the device is turned on. Some devices can get away with not needing a reboot sesh, but this is the general rule explained with BobjGear and their Android ethernet adapters.

Secondly, another very important detail, is that sometimes, you need to manually configure the adapter and its ip address through ADB or Terminal Emulator. The commands follow this format, as described in this article:

ifconfig [eth0|eth1|eth2|etc] [IP] netmask [NETMASK]
route add default gw [GATEWAY] dev eth0


ifconfig is not a typo. You will have to figure out which network "slot" your dongle is attached on via netcfg. It will list all network components in use or idle, usually wlan0 is built-in wifi, rmnet listings are mobile data, and p2p0 is VPN. Your dongle will probably fall under eth0 or 1, or wlan1 or 2.

Finally, if all else fails, you may need to find an adapter that either a) has matching (or close to matching--starts with RTL8) chipsets, or b) a (Android/linux-confirmed) truly universal wifi dongle.

If that cannot be done, this XDA post explains how to modify a Nexus CM11 kernel (your lucky day) via modprobe to enable additonal drivers. You may want to contact him for help, as his flashable kernel is specific to a custom CM11 ROM posted on XDA, just to match the checksums.

Good luck!