Planting grass seed too early (as well as too late) can result in a lawn with gaps because the seeds die off or become unproductive. Not only do they need certain temperatures to germinate, seeds also require a specific amount of time to grow mature enough to survive.
Each type of grass has its ideal planting time. The earliest you should plant cool-season grasses is early spring. Warm-season grasses can be planted in late spring.
The closer you are to the expected frosts, the more probable there could be problems. You can plant grass seed outside the recommended times, but they may rot from the excessively cold or wet soil or they can be killed from late spring frosts.