The US Air Force has a goal of qualifying all of their aircraft to fly on biofuels by 2011; they've flown B-52s and other aircraft on 50-100% biofuel mixtures. Currently, most biofuels for aviation use cost several times what petrochemicals cost, but I could definitely see this changing. It's actually pretty easy to get a jet turbine to run on anything, but the difficulty is more with qualifying the entire storage/supply chain to be stable, and stability at temperature extremes. If the Air Force can transition to biofuels, it will be relatively easy for scheduled commercial flights to transition.
Given relatively cheap electricity to input, there are plenty of processes to make liquid hydrocarbon fuels -- algae biodiesel, some forms of intensive agriculture, and CO2 sequestration from the air, as are pointed out in the article. These would be "carbon neutral" in terms of atmospheric CO2 as well.