The last thing that I had heard on this is that most of the technology already exists for this. The main thing holding it up is the development of long enough carbon nanotube cables. But I cannot say that I have been reading all the research or anything
, just a nerd at heart and this is a really cool idea.
I had also heard that the trip would be a matter of something like 3 days and if they wanted to transport humans they would need to build shielded cars for the journey so you do not get cooked once you leave the atmosphere.