Electrolysing water to make H2 and extracting CO2 from the environment, and then synthesizing hydrocarbons from them, is extremely energy inefficient.
Sure, theoretically, it can be done, and maybe one day it could even be done efficiently. But Tesla is making battery-electric cars that work today.
The military does not care about efficiency because they have nuclear reactors on their ships and their goal is to not to have to transport liquid fuel.
Tesla's cars are wildly price inefficient because they cost $100K. For 10K you can get a decent car that has 4 times the range. http://en.wikipedia.org/wiki/Tesla_Roadster
How many gallons of fuel can you get for 90K?
They are nice toys for rich people. Perhaps there is a market for that. Good luck to them.
But for mass transit unless you can get the price of the batteries to plummet it just does not work.
A mass-produced commuter could be much cheaper, but there's a huge risk. Tesla aims to reduce the risk by validating the market, solving technical problems, creating infrastructure (recharge stations) and solving social problems (convincing people that range doesn't always matter, and educating them on the strengths and weaknesses of electric cars).
A low total-cost (including fuel and maintenance) electric car can probably be produced, but it's not the Tesla's top model.
This doesn't eliminate the tail (we still have to deliver ammunition, lubricating oil, food etc. to the fleet) and it doesn't eliminate replenishment at sea (we still have to get that stuff from supply vehicles to ships), but it does lighten the supply load and create more military options.
Lots of people killed by IEDs on long supply lines in Afghanistan is an extreme example of the human and military costs. Some of those died to fuel A/C for uninsulated tents... madness.
1) uranium -> nuclear power -> expensive synthesis -> local transport -> fuel
2) uranium -> nuclear power -> transmission lines -> charging batteries
3) crude oil -> refinement -> transport -> fuel
EDIT: Found a reference from another comment: http://en.wikipedia.org/wiki/Fischer%E2%80%93Tropsch_process... It says that the input energy is 2-4 times the stored energy for synthesized hydrocarbon fuel.
Instead of the energy system, consider the cost of military supply lines. There's more than the financial cost of delivery; long supply lines are vulnerable to attack and disruption. You don't need to imagine an example: consider IEDs in Afghanistan. Many of those were trucks delivering food and fuel to bases. Efficiency (i.e. insulating tents so less fuel is needed for A/C) results in less deliveries and less deaths.
The same principle applies at sea. Oil ships are a vulnerability and another thing to plan, as well as a major cost that can be more important than the energy efficiency issues.
Telsa, like many startups, is pursuing a low-volume, price-insensitive market first. That helps pay for all sorts of startup and R&D costs, and lets them work out issues before they scale. Their long-term goal is, per Wikipedia, "eventually mass producing fully electric cars at a price affordable to the average consumer".
There are several fully electric vehicles in production that cost $35k.
http://en.wikipedia.org/wiki/List_of_production_battery_elec...
They have a substantially lower cost of operation than gas-powered vehicles, so they are plausibly cheaper to operate over the lifetime of the car:
http://en.wikipedia.org/wiki/Nissan_Leaf#Operating_costs
And over the long term, expecting batteries to get better is a pretty good bet. Everybody from Apple to Toyota is eager for battery improvements.