I got this achievement with 4 hours to spare. Follow these steps and you shouldn't have any trouble.
I recommend not trying this until you're at least level 30.
1. First off, you'll need $2 million for the SUV keys. You can get this in about an hour using the 3 gambling books and the big slot machine in the Slot Ranch Casino. See the Big Spender achievement solution for more details.
2. When you have $2 million, save your game at a restroom then choose Quit > Restart Story from the pause menu and select the save file you just made.
3. Complete the 1st case (Find Katey Zombrex) then complete One Man's Trash to open the pawn shops.
4. Go to the pawn shop on the Sliver Strip and purchase the SUV keys. Make sure you pick them up.
5. Now, this is really important. SAVE then Quit > Restart Story like you did before.
6. Run straight to Bennie Jack's BBQ Shack in the Americana Casino and grab the Driving book then get to the SUV in Shamrock Casino on the Silver Strip.
7. You should have around 4 hours before the 72 hour countdown begins, so make the most of it. Obviously, skip all scoops and case files.
8. Drive up and down the Silver Strip / Fortune Park / Platinum Strip area running over the hordes of zombies. Speed really is the key here to get maximum kills. Don't run head-on into a wall just because there's a huge cluster of zombies in front of it. The time it takes to get back up to full speed isn't worth it and zombies you didn't hit directly with the SUV (knocked over by other zombies) will just stand up again.
9. Eventually, the zombies will start to thin out so SAVE your game in the middle of Fortune Park then RELOAD that save. This will restore zombies to their original numbers and reset the SUV. I saved every 2500 - 3000 kills.
10. From the Save door, head right then turn left towards the Fortune City Hotel and you will see a buggy parked outside. Jump in and drive back to the SUV. Repeat from step 8.
Never leave the Strip / Park area. You don't want survivors or psycho's spawning in that area as it thins out the zombies. You also have to endure two loading screens. Instead, always use the save / reload method described above.
After you get the SUV keys, restart story, then all you need to do is get the driving book and get to the SUV. Doing this you'll have an extra 4 hours before the 72 hour countdown even begins.
Use all 3 save slots incase you mess up.
Those of you not sure on what route to run, there are many options but I highly recommend something similar to LeonDMSmith's which can be found here:http://tinypic.com/r/2nu29ms/7
The small corridor between the Americana and Cash Gordon casinos can net you 50 kills. Just try to hit reverse before you go down the stairs!
Time / Kill Goals
Note that Day 1 is only 17 hours long, hence a short Day 4 in 72 hour mode.
Day 1 - 7pm - 10000 kills
Day 2 - 7am - 22000 kills
Day 2 - 7pm - 34000 kills
Day 3 - 7am - 46000 kills
Day 3 - 7pm - 58000 kills
Day 4 - 7am - 70000 kills
Day 4 - 10am - Game over.
If you keep in front of these, you're golden. If you're only 1000 kills behind these goals by Day 3, you should still be ok.