Try leaving 5 minutes earlier, then 10, then 15. Sometimes there will be a miraculous "break point" where leaving earlier than the point gets you to where you want to go significantly faster than the difference in departure time.

When I was just out of high school as still living at the parents house, I took the mandatory job at West Telemarketing (I think they have offer letters printed on the back of all high school diplomas in San Antonio). The break point was 7:17a. If I left before this time, I could be at work in 15-20 mins. If I left even 5 mins after that? A 30-35 min ordeal.

If you can manage to pry yourself off the bed a few minutes earlier, it might be worth it to try. But I do have to mention that I don't exactly practice what I preach. I'm skidding into the parking lot a minute before work starts.