I wouldn't say "no hope" but I think it's rather scarce. Look, folks, if you really take a look at human history, no, we don't always find solutions. We're very bad about wearing blinders until we get ourselves into a corner and huge masses of people suffer/die because of it. And we've scarcely been on the planet 5 million years as hominids, let alone any sort of "civilization". Where that's concerned, we've taken, what? less than 4 millennia to cause global muckups some of which simply cannot be corrected and those which can will take literally thousands to millions of years to set right -- and we aren't likely to be around to see it.
As for colonization -- I'd love to see it. Ain't gonna happen anytime soon. Does anyone here remember the experiment in the Arizona desert where they tried creating a small colony of supposedly compatible scientists? The project was supposed to last for 5 years. In just over 2 it went so sour they had to dismantle it before someone literally ended up committing murder. Put people into the close confinement needed for colonizing in space, enough to avoid the dangers of endogamous breeding, and you're looking at bloodshed, most likely massacre or extinction. Unless, of course, we can actually make a workable cryonic system and sophisticated enough technologies to allow a ship to pilot itself to whatever destination, set up the colony, avoid any unforeseen hazards along the way, and then go "wakey, wakey" to the human cargo. Then, given the above problems, it would be transferred from the trip to the actual colony -- BUT, if we are able to spread them out fast enough via terraforming, and send replacements quickly enough to make up for the losses along the way due to accidents, unforeseen dangers (again), flareups, etc., it MIGHT have a chance of surviving. One colony. One. Out of how many? billion by that point? (And, on the subject of world population, when I was in high school in the mid-70s, the figures stood at just over 3 billion. In 30 years, we've doubled that. We're growing at an exponential rate, people; and the human race ain't gonna stop breeding any time soon. The estimates are that, within 50 years, we're likely to top 12 billion; I'd say 15-20. Anyone think that, with what we're doing to the planet, it's going to be able to support that sort of number?) Not to mention the bottleneck of expense, and people who feel we need to be spending the money on problems here rather than spending huge amounts going "out there" (not realizing, perhaps, that it's part of the same problem in the long run; but quite right that in the meantime people are starving unnecessarily).
Will the human race adapt? Probably. But this isn't the only thing we have to be concerned about. Supervolcanoes, for instance. We know of at least 3; one of them, they expect, is due to go sometime in the next 3-5 centuries. The last time that happened, Europe's population was something like 10,000,000. Once it was over, it was down to around 500,000. That's a pretty serious drop, wouldn't you say? (And they had a lot less people and a lot more natural resources per capita than we -- at least until the ash and nuclear-winter-style climatological changes began to tip the balance.) And the possibility of near-earth objects actually not all being discovered, and one maybe connecting, can't be ruled out, either. And blowing 'em up doesn't help, because then you just end up with lots of little buggers spread out coming down. Anyone around here seen the effects of a shotgun blast? Now magnify that by a few thousand times in the size of the projectiles, not to mention the velocity/impact.
And then there's just plain greed. Even the most enlightened people are reluctant to give up their comforts; say air-conditioning when it hits those 100+ days... We've seen what happened in Europe when things got a little warmer than usual the last few winters. Not to mention the number of elderly folks and babies that expired over here due to the heat.
And so it goes.....
No, it's not hopeless; but it's pretty bleak. And it certainly isn't something that any of us can afford to just sit back and feel smug about. The piper's been toting up that bill for a long time, and I'm afraid he's about ready to start collecting.....