In the event you need to renew a passport on short notice, the United States Department of State does have a procedure where you can request an expedited renewal. A regular expedited request will take about two or three weeks instead of the normal four to six weeks. It does cost more than a regular application.
Fill out all of the necessary forms for a passport renewal. See the travel.state.gov website for details for the current renewal requirements.
Write "Expedite" in large letters on the outside of the envelope containing the passport renewal application.
Include a personal check or money order for the expedited service, which cost $60 as of 2011, plus the regular processing fees and overnight delivery costs.