I wouldn't say it's that far off at all. All of the component technologies are already present, and really have been for decades. The first NASA flyby plan of Mars was planned in the mid 60s, and set for 1976. It was scuttled due to budgetary issues.
The only problem is $$$ and risk. We're happy to casually spend hundreds of billions of dollars on obscure geopolitical goals half way around the world, but fight nickle and dime for visionary goals that might genuinely positively reshape humanity. And the other issue will be risk.
Most early colonists will, in all probability, not meet pleasant ends - like literally every colonization effort, ever. And so it's important to have a society that can recognize and praise them for their bravery, try to prevent what killed them from killing the next batch, and immediately continue carrying on.