It's believable if it's set in winter somewhere cold. Otherwise yeah, if it hasn't been established that the car does that sometimes, it's bs. And if that has been established, it's pretty heavy-handed foreshadowing.
I was going to say these people aren't old enough to remember the time before fuel injection. When you could coax a car to start after multiple failed attempts but don't flood it or you're going to be sitting there a while.
As Yoda says, “start or start not, there is no try 14 times and then the problems randomly fixes its self just as the killer breaks the windows or whatever”