quickest way to get passport (daughter lost hers)

I have always used the official government web site. The one time I had to renew in a hurry, I used the expedited service and it only took 10 days even though I was expecting it to take 20 days, but my background isn't unusual in any respect. Got the new photo's at a Walgreens drug store.

Here's a link to their page: Expedited Passports