I'm not familiar with Cornyn, and don't know what his motives here might be. I believe he is fairly new to the Senate, and was a prosecutor before being elected, so it seems he wouldn't owe Specter anything. Maybe he's toying with him, maybe he's looking to get in the papers . . . hard to say.
I'm comfortable with the knowledge that the committee votes secretly, then it goes to the entire caucus, who also has a secret ballot. Specter doen't have many friends, and I think his chickens may be coming home to roost at last.
Someone on another thread the other day wrote that the committee Republicans vote in an open election, not secret ballot. And then the GOP Senators then vote by secret ballot to accept or reject the proposed chairman.