Its a great idea, this video has been floating around for a couple of years in various forms. The big hurdle they need to overcome is harvesting this in an efficient way. When I saw them on a TV show they said they haven't come up with that yet. Also, what are the energy inputs required. Like I said... great idea, but still some unanswered questions.
It will, as soon as it becomes price competitive with gasoline made from crude, which may happen earlier than many people think. The government could care less, as long as gasoline is cheap. The oil companies, well, some are already in the bandwagon, i.e.: Alternative energy | Environment and society | BP
Harvesting can be done with a filter or a centrifuge, they both much simpler and require much less energy than what's needed for traditional crops like corn or wheat. As for energy inputs -- the Sun is still free. Some other people are using the flue gases of a coal fired power plant for extra dose of CO2 and heat; the latter can be very useful in a colder climate.