Well there is a certainly a lot of doom and gloom predictions, God help the aliens
We should take into account the effect that the revelation of alien life elsewhere in our Universe and the possibility of interstellar travel, will have on us. Also the appearance of a sudden, shared and definite fate for everyone on this planet may be a great unifying factor across nations. One can go by history to judge human behavior when faced with a common impending disaster that can suddenly equalize everything else. There has been only one other such a possibility and that's the possibility of global nuclear war or nuclear
holocaust 
.
Have we pressed the button yet , no!. So what does that tell us, it tells us that inspite of a reptilian core in our brains, our humanity can intervene with reason and compassion when faced with a common cause.
Furthermore we have to take into account mindsets of people. There would be an urgent need to get off the planet and probably out of the solar system in a hurry. That would lead to funding and efforts to be completely diverted to technologies relevant to space travel with the bare minimum kept aside for the time life needs to be sustained on Earth.
Suddenly it would be possible to validate a lot of theories and ideas regarding space travel that may never have been tried for the next 100 years. I think many scientists would want to see the successful culmination of their lives work. Especially if it results in the construction of projects like Orion or similar that gets a large number of people off this world. Or they would die trying. There may be unforeseen engineering challenges to building the Orion that may need brilliant and bold steps to resolve.
Furthermore, there would be others who would prefer to stay on Earth and face the disaster rather than take the giant leap in courage and faith required to adapt oneself to an alien world(one cannot even begin to fathom the sheer amount of courage that would be needed). These people would just continue with their daily lives and would contribute to efforts on the ground.
Also the aliens may have given up on saving our planet. But we wont(not may be we wont, we wont

). Every theory, even the wildest ones, every ounce of reason and mathematics, each and every resource at our disposal and on this planet would be committed to saving it. And we may find a way. Even 10 years is a long time, especially if a billion minds start working on the same problem, there is no knowing what may happen.
Lets not jump to conclusions about getting off this planet therefore

or that we will all drown amidst mass hysteria ! We are probably in the most peaceful period of our civilization in all our history. There is a lot of reasonable people around and when it comes to light that this problem cannot be solved with money or wished away, and reasoning alone can solve it, then each one of us would be forced to rethink our lives and decide what to do.