They actually had a second shuttle already on the launch pad, ahead of schedule for prep for the next mission.
Wikipedia quote time: "The CAIB [Columbia Accident Investigation Board] determined that a rescue mission, though risky, might have been possible provided NASA management had taken action soon enough.[56][57] They stated that, had NASA management acted in time, two possible contingency procedures were available: a rescue mission by shuttle Atlantis, and an emergency spacewalk to attempt repairs to the left wing thermal protection.
Normally, a rescue mission is not possible, due to the time required to prepare a shuttle for launch, and the limited consumables (power, water, air) of an orbiting shuttle. However, Atlantis was well along in processing for a planned March 1 launch on STS-114, and Columbia carried an unusually large quantity of consumables due to an Extended Duration Orbiter package. The CAIB determined that this would have allowed Columbia to stay in orbit until flight day 30 (February 15). NASA investigators determined that Atlantis processing could have been expedited with no skipped safety checks for a February 10 launch."
56: Columbia Accident Investigation Board (2003). "Decision Making at NASA" (PDF). CAIB Report, Volume I, chapter 6.4 "Possibility of Rescue or Repair". p. 173ff. Retrieved March 28, 2013. http://anon.nasa-global.speedera.net/anon.nasa-global/CAIB/C...
57: Columbia Accident Investigation Board (2003). "STS-107 In-Flight Options Assessment" (PDF). CAIB Report, Volume II, appendix D.13. p. 391ff. Retrieved January 30, 2006. http://www.nasa.gov/columbia/caib/PDFS/VOL2/D13.PDF