As much as I would like to vote yes, I´m afraid I have to say No.
Technological, it might be possible, but, as others allready said, the political will just isn´t there.
It would take a real revolution of society to make a project happen that will cost billions (and I am talking about european billions* without a large majority of people screaming bloody murder and pointing to all their pet peeves that should get at least a part of that money.
Only way I can see this happening is a major event (think the movie contact, for example), that would unite the people of earth behind a "vision" or "dream"
*this means trillions in US-english (is this in british english too?)
Edit:
As welchbloke said, we are not exactely a represantative sample. On the other hand, if you asked a representive sample, I´d guess 90% of the people wouldn´t know what the hell you are talking about.