Supersonic flow and high-bypass fans don't get along well. The power is probably there to get something like a 777 to just ofver the speed of sound (maybe with a dive), but fans produce thrust with a relatively low pressure differential (think EPR, but not). Once you've got flow being mechanically compressed at the face of the fan, the engine has to work a lot harder to generate a sufficient differential pressure to keep pace. Supersonic flow is not as big a deal for a turbojet, because all the air going into the engine is going to be compressed to pressures several times higher than you could ever hope to get with supersonic flow stagnation.
I have a sneaking suspicion that this was a major hurdle for the Sonic Cruiser. You'd have to have engines that can get you off the ground in 6,000 feet (fans are better at this), but still get you 6,000 miles away at trans-sonic speeds (jets are better here).