I think the courts will invalidate it,” Specter told me. “They’re not going to give up authority to decide habeas-corpus cases, not a chance.” Others are less sure.

“It’s a pretty odd position for Specter to take,” Amar, of Yale Law School, said. “He trusts the courts to take care of a problem when he’s voting for something that strips them of their jurisdiction to do it. It’s like saying, ‘I shot at her, but I knew I was going to miss.’”

This is a good overview of the politics behing the MCA. As for Specter's "odd" position, shit ain't checkers man, its chess.

The New Yorker: KILLING HABEAS CORPUS