People used to think going over 50 mph would kill you, and thought heavier then air flight was not possible.
We have a big difference here, though. The assumption back then was mostly due to "common sense" (most people just could not imagine going that fast) and religious superstition (the steam engine as an infernal machine).
There was however not a single serious scientist that would have supported the notion. There were enough animals RUNNING at above 50 mph that proved that a biological organism is not only fit to endure, but even to produce such speeds.
The FTL-thingy is a bit different... we simply don't know ANYTHING that goes above the speed of light, and the theory of special relativity shows quite clearly that the light-barrier cannot be broken by conventional means (simply going faster).
So if there is a solution to FTL, it has to be found in an area of science that we have not discovered yet (parallel dimensions, hyperspace, wormholes and all that stuff). It is pretty much proven that going faster than light physically in our universe is not possible. Wheather or not someone will discover a means in an area we might not even know about yet is very speculative, but it could happen. If there IS a possibility, I'm confident that sooner or later somebody will find it. But the possibility exist that nature indeed forbids us to cheat us through this one...