I've been watching Vsauce for a couple of years. But, I think it may take half or even a full century for humans to make it out of our solar system. We currently have no energy source powerful enough for humans to do interstellar travel neither do we have the knowledge how to survive so far from earth without essential needs like water, oxygen and food.
There are some research papers that propose methods of exceeding the speed of light (http://en.wikipedia.org/wiki/Alcubierre_drive) and a few more, but if they are possible to work in the real world and not just theoretically, we might be able to travel there in our lifetimes at the rate technology has been moving forward.
On the other hand, even with FTL travel we probably won't be able to because it would take forever, still. We'd have to go like 5x times the speed of light to make it feasible, because transmitting data wouldn't be a realistic concept, so when some brave people left, we wouldn't know anything until they arrived back.
Relatively speaking, food, water and oxygen are the least of the problems with interstellar travel, and pretty much solved.
There's just so many barriers to cross, but if we can get the traveling part down, I think it's possible. Else, no chance.
If it's possible, why hasn't anyone visited us? They could easily make Von-Neumann probes to visit every planet, or something similar. We've had a very visible electromagnetic footprint for over 100 years. If any sentient being exists, the best way to explore the world would be to put a probe in every solar system. It's kinda mind boggling. Maybe we're the only "highly intelligent" species in our galaxy, and intergalactic travel isn't possible.