It's all going to work out.
I think ways of putting people into suspended animation will be developed over the next several decades. This will allow colonists to sleep away the decades while their ships are in transit.
The technology exists now to build ships that can go .2c, but we lack the will as a society to follow through. Once CATS is developed, then I think private individuals and groups will fill the vacuum and begin moving out into space on their own. Once that happens, there'll be no stopping the migration to the stars.