Back during the VC-25 development, I was in some real entertaining meetings with the USAF. Lots of questions about taking off with various systems failed. Basically, they were worried about the ability to get the President out of Dodge in a hurry, even if they had a broken airplane.
While I doubt you'd ever get them to admit this - I do think they want the to ability to depart even if they have a failed engine. The 747 has AFM procedures for a 3 engine ferry - with aerial refueling they could take off light, then aerial refuel and fly to pretty much anywhere they wanted. I'm pretty sure you wouldn't want to try that with a 777.
HH - I certainly hope we still have the engineering for some of the special mods from the VC-25 that would be applicable to a new 747-8 based AF1, although it wouldn't surprise me if much of it's been lost to the sands of time (VC-25 also has a really trick airstairs setup that deploys out of the cargo deck, with stairs up to the main deck).