The search is already very much on for finding a second Earth! We have a finite time here, whether due to the destruction of the Sun or impact from an asteroid. I don’t think space is the issue, more that we will run out of resources at the rate we’re expanding.
Yes, if population growth doesn’t slow down or stop, we’ll reach that point within a few generations – scary stuff!
Already, we use more food and electricity than the Earth can sustain. If everyone in the world lived like the average person in the Western world (e.g. America, Britain and the richer parts of Europe) then we’d need FOUR planets to support us all.
So we definitely need to find another planet to colonise, and fast. But however fast we go, it will still take too long. What we really need to go is start taking better care of the planet we’re on, and fast!