First: liquid hydrocarbon fuels are hugely useful for a number of characteristics.
They're very energy dense, by both weight and volume. They've over ten times the energy storage density of batteries, and while they have lower energy density by unit weight than hydrogen, have over seven times the density by volume with vastly fewer handling constraints. They're easily handled (no high pressures, low temperatures, corrosion, embrittlement, or other issues). They're generally really safe -- many liquid hydrocarbons won't explode unless specifically induced to do so. They're a drop-in replacement for existing fossil fuels. They could be blended with these, and can utilize the same processing, transport, and utilization infrastructure. Engines would not have to be modified. At the same time, for those who see efficiencies in electric drives, they're amenable to hybrid-drive technologies. And we've got well over a century of expertise in utilizing them.
For transportation, liquid hydrocarbons are very hard to beat, and for certain modes, all but essential, especially heavy land cargo, marine shipping, and air travel.
The research that the US Naval Research Lab is conducting is based on over 50 years of work on the concept, with the first studies undertaken by nuclear physicist Meyer Steinberg at the Brookhaven National Laboratory in 1964. Steinberg continued his research through the 1990s, with further work at M.I.T. under Michael J. Driscoll and more recently as USNRL (who peculiarly fail to cite the earlier research -- it's rather like an evolutionary biologist failing to credit Darwin). Steinberg's work generally considered nuclear power as the electricity source, though any generating option could be substituted. More recent research considers nuclear, solar, and OTEC, an ocean thermal power system.
The basic concept was suggested by M. King Hubbert, the petroleum geologist who predicted peak oil in the 1950s, in a 1962 report (though he suggested mining carbon from limestone).
In terms of process, there are two very-well understood processes operating at industrial scale presently, hydrogen electrolysis and Fischer Tropsch synthesis. The third stage is where most research is focused: on finding means to sequester carbon from seawater. A small fraction is present as dissolved CO2, but most (about 96%) is in the form of dissolved carbonate and bicarbonate.
Since carbon is being drawn from the biosphere (seawater), it's overall carbon neutral, though it might tend to bias balance slightly toward the atmosphere as compared to the oceans. If run in excess of human energy needs (a very expensive proposition), it could sequester additional carbon from the atmosphere.
The primary energy cost is in the electrolysis, which returns hydrogen with about 60% of the energy capacity as the input electricity -- so your conversion costs you energy. Fischer Tropsch processing is exothermic (more energy is released than consumed). Energy usage of the CO2 separation phase is comparatively low, much of it is in the water handling -- you've got to move a lot of seawater to get the carbon necessary. I suspect overall efficiency will be roughly 50%.
Though the Navy research is looking at this for their own purposes, it could just as well be used for civilian purposes. The 100,000 gallon/day capacity seen for a carrier task force would be roughly appropriate for a city of 100,000. My own cost estimates, including solar power provisioning, are higher than the Navy's, about $9/gallon. But that would be a stable price going forward -- with a renewable liquid fuels source, there are no oil embargoes, supply shocks, or imports.
At a national scale for the United States, supplying 20 million barrels/day, you'd require 2TW of power -- a solar collection region about 180 miles on a side. That's quite large, but as compared with biofuel-based alternatives, downright reasonable -- most plant-based fuel proposals if scaled out would require a sizeable fraction, or several multiples, of total US land area to provide an equivalent of present petroleum usage.
On the "bad news" front: the fact that research has been conducted in this area for 50 years without significant implementation suggests that there may be engineering or other challenges which are frustrating broader application. Or it could be that fossil fuel prices have simply been too low to allow larger-scale demonstrations.
I've explored a few other aspects of this in a series of reddit posts covering the USNRL's work and other historical background.
Search on "fischer tropsch": http://www.reddit.com/r/dredmorbius/search?q=fischer+tropsch...
USNRL research and papers: http://www.reddit.com/r/dredmorbius/comments/22k71x/us_navy_...
BNL/MIT history and papers: http://www.reddit.com/r/dredmorbius/comments/28nqoz/electric...
M. King Hubbert connection: http://www.reddit.com/r/dredmorbius/comments/298a4l/seawater...
And for comparison, limitations on biofuel potential:
http://www.reddit.com/r/dredmorbius/comments/28k1w5/prospect...
http://www.reddit.com/r/dredmorbius/comments/2cvap7/the_intr...