Rohrabacher continued: "Heroes are heroic people because they risk great suffering. But how we deal with this heroic person ... what we do now will be defining ourselves, our own character." 

He said that not only would it be "immoral and cowardly" to abandon him, but it would also deter others from working with the U.S. in the future. 

The Obama administration claims it's been pressing Afridi's case with Islamabad all along. 

"We have regularly taken up this matter with Pakistan. I would expect we will continue to," State Department spokeswoman Victoria Nuland said. 

Rohrabacher said he assumed there was "quiet diplomacy going on" in the aftermath of Afridi's arrest. But he questioned whether the case fell through the cracks. 

"Unfortunately, there are so many things on the plate for these guys to be doing quiet diplomacy about (with Pakistan) that the plate's a little overloaded, that it might just have fallen on the ground and broken," he said.