Kill the crazy science geek and then after that you should find the death machine.

When you have got it, get yourself downed and get someone else to revive you.

When you get up, the Death machine timer will be gone, but you will still have it.

Note: Once you have done this, the gun uses up a slot, and can be swapped, traded, etc. I am not sure if you can upgrade it but I doubt you can! This only works on co-op!