According to http://en.wikipedia.org/wiki/Certified_first_responder
“A certified first responder is a person who has completed a course and received certification in providing pre-hospital care for medical emergencies. They have more skill than someone who is trained in basic first aid but they are not a substitute for advanced medical care rendered by emergency medical technicians, emergency physicians, nurses, or paramedics. The term "certified first responder" is not to be confused with "first responder", which is a generic term referring to the first medically trained responder to arrive on scene (police, fire, EMS).”
“The U.S. Department of Transportation (D.O.T.) recognized a gap between the typical eight hours training required for providing advanced first aid (as taught by the Red Cross) and the 180 hours typical of an EMT-Basic program. Also, some rural communities could not afford the comprehensive training and highly experienced instructors required for a full EMT-Basic course. The First Responder training program began in 1979 as an outgrowth of the "Crash Injury Management" course.
“In 1995 the D.O.T. issued a manual for an intermediate level of training called "First Responder." This training can be completed in forty to sixty hours. Importantly, this training can be conducted by an EMT-Basic with some field experience—which is a resource available "in-house" for many volunteer fire departments who do not have the resources for full EMT training. The first responder training is intended to fill the gap between First Aid and EMT-Basic.
“The American Red Cross conducts a course titled "Emergency Response" that fits this definition.”
The Department of Homeland Security is committed to helping first responders nation-wide by ensuring that emergency response professionals are prepared, equipped and trained for any situation, and by bringing together information and resources to prepare for and respond to a terrorist attack, natural disaster or other large-scale emergency.
I see nothing above or in the Constitution that the US Government should pay the medical bills for the 9/11 First Responders.