This is currently running on the National Geographic Channel. The premise is that a neutron star is going to decimate our solar system - including the Earth - and Humanity has 75 years to build a starship using current/near future technology to whisk a quarter of a million "chosen survivors" off to Barnard's Star - 6.5 or so light years distant.
It is a documentary with short vignettes acted out to illustrate various concepts and possible events. At its core, is a huge multi-national governmental project to build a giant starship which will transport a genetically "perfect" and bio-diverse group of humans on a 50 year interstellar journey to their new home - Earth II.
Of course, this isn't the only project underway...
Private multi-billionaires have pooled their sources and are building their own starship to escape the upcoming doomsday. They, are selling tickets for the price of $500,000,000 a piece. And, of course, unlike the government funded program, the people who actually design, and build the starship have already earned
their passage to the stars.
The Government funded project succeeds and the privately funded project blows up on the launch pad!