I love what Brian Greene said: "We'd be thrilled if it's right because we love something that shakes the foundation of what we believe. That's what we live for."
The title is a bit exaggerated though. Discovering that a sub-atomic particle (neutrinos in this case) travels faster than the speed of light does not destroy Einstein's Relativity theory. We know that Relativity explains very well gravity and space-time at the macro level. And it's been a generally accepted view for a long time that Classical Relativity breaks down at the sub-atomic level.
However, for now, people are still skeptical about these findings. As one physicist stated, "This is ridiculous what they're putting out. Until this is verified by another group, it's flying carpets. It's cool, but..." And Brian Greene even added: "I would bet just about everything I hold dear that this won't hold up to scrutiny."
Having said that, if indeed neutrinos could accomplish such a feat, this only mystifies further our picture of the quantum world and may hint at the existence of extra dimensions. The universe is indeed stranger than we can imagine.