The car in question is the ice cream truck, which will hold eight passengers. On the first day, it is located near the Slot Ranch Casino.
This solution isn't hard, but it's a bit time-consuming. You may want to use a separate save slot for it, just in case something goes wrong.
On the first day, make sure to have all cases cleared prior to 3 PM, when the "People Like Us" call comes in. This is a psychopath fight, so come prepared.
After "People Like Us" is done, head up the Silver Strip towards the Yucatan Casino. You'll find Chad here, fighting some zombies. Clear them out, and then get Chad to join you.
Take Chad down towards the Arena. During this time, you'll probably get the call for "Brains Over Brawn" (4 PM).
Meet up with Doris in front of the arena. Get her to join up, and then set the guide arrow for "Brains Over Brawn," which is in the hotel. With Chad and Doris in tow, enter the hotel and follow the arrow. At some time during this procedure, you'll get the call for "Art Appreciation" (5 PM). Don't worry about it just yet.
In the hotel, you'll find John, Curtis, Kevin, and Brian playing a game. Get them to join you; they'll join up quicker if Doris is nearby.
At 6:30, you'll get a call from Stacey, asking you to come back to the safe house. There won't be much time, but you'll still make it since the safe house isn't far from the hotel. Make sure everyone is following you and head over there.
Important: DO NOT take the survivors into the safe house with you. Have them wait somewhere nearby instead; direct them to stand well away from the vent before going inside. Make sure their health levels are up, since they'll start losing health when you go in the vent.
Do what you have to do inside the safe house, and then quickly head back out through the vent. Heal up your survivors with food, and then set the guide arrow for "Art Appreciation," which is in the Palisades Mall, upstairs in the gallery.
At 8 PM you'll get the "Once Bitten" call, most likely while you're en route to the Palisades. We'll be coming back to that one momentarily.
For "Art Appreciation," get Randolph to join you by buying his painting. If any of your survivors are low on health, heal them up with some of the wine in the gallery, or next door in the booze store.
If you don't have any Zombrex, buy some from the pawn shop near the art gallery.
Set the guide arrow for "Once Bitten," and lead your group of seven towards the Silver Strip, where Jared is located in the Pub O' Gold. Jared won't join until you give him some Zombrex, so give him the supply you just bought. Jared moves slowly, so offer him your shoulder.
With all eight survivors in place, head towards the Slot Ranch Casino and the ice cream truck. Press B to get in the driver's seat, and all the survivors will pile into the surprisingly roomy back seat. As soon as the last person gets in, the achievement will unlock.