I'm taking a more idealistic approach to how humanity will act after the end of the world. I'm probably not going to get a lot of support for that decision, but I really don't care.
Anyways, building off of that assumption, we assume people put aside their petty differences to make their more or less miserable lives better. They find that they, theoretically, could follow a starship which they believe found a new paradise for humanity. They don't know New Terra blows (of course, if the Blight has died off by the time they arrive then theoretically it may be a pretty nice place). So the survivors on Earth scrape together everything they can to get the new starship (aptly named the Hope) operational. Of course, it's of lower quality than the original, so less people are brought and its various other systems are of lower quality than the original Conestoga. This explains why they take so long to reach New Terra (among other things).