"Your immediate attention to this issue is needed and appreciated."

Toomey explained that in 2000, HHS required that organ availability must be based on medical necessity instead of the order in which organs are requested. However, the Organ Procurement and Transplantation Network (OPTN) imposed a process that only applies to patients 12 and older.

"Sarah is therefore ineligible under this system, despite the fact that she is a top priority on the pediatric list," Toomey wrote.

Toomey added that the hospital has asked a national group of transplant physicians for an exception, which would allow Sarah to move up on the list. However, he said that group denied the request.

Because HHS oversees OPTN, Toomey asked Sebelius to do "everything you can" to help get Sarah a lung as soon as possible.

Sarah lives in the district of Rep. Pat Meehan (R-Pa.), and Meehan has also pressed to change the policy that has so far prevented Sarah from getting a transplant.

Meehan also sent a letter to Sebelius on Tuesday that calls on her to convene a meeting of the OPTN to deal with the issue.

"I am requesting that you convene an immediate meeting of the Board or its Executive Committee to address this tragic unfairness and act to give Sarah a chance at life and an adult lung from the next available donor," Meehan wrote. "Sarah's young life literally hangs in the balance."

— This story was updated at 4:35 p.m.