If he appointed McCain for political but not practical reasons, that would work. McCain will soon die, and Obama gets the credit for the appointment, but none of the grief from having him serve.
Among Senate Republicans I could see Chuck Hagel at Defense or Homeland Security, or Dick Lugar at State; but I think McCain pretty much took himself out of the running for an Obama Cabinet seat by the kind of campaign he ran. It wouldn’t reflect well on either of them for Obama to reward McCain with a Cabinet post. As for Lincoln, remember that he appointed fellow (although rival) Republicans to his Cabinet; he didn’t appoint Democrats, with the sole exception of Edwin Stanton as SecWar (and even then, only after GOP appointee Simon Cameron flamed out).
A Wiki list that may be of interest: List of United States political appointments across party lines - Wikipedia
Lincoln didn’t exactly have a choice. First off he had made deals with his rivals for the nomination that they be included in return for their support. And he won with what? Not even 40% of the vote? If the Democrats hadn’t split apart they would’ve likely won even without accounting for the Constitutional Unionists. He absolutely needed to get his opposition in his tent. He knew what he was in for.
And having written that I see the parallel … Obama also knows the situation he is in for and appreciates the value of having the opposition in his tent. Still I I can’t see a cabinet role for McCain. I could see him carrying water on a cap and trade bill however.
He could always appoint Palin. She would be a plus to any administrative position with her great experience and all.