I felt he saw it as something akin to "a stitch in time saves nine." While the level of panic he had didn't make sense compared to how far along the crisis would be, other charcters, most notably Leon, saying "We can put it off until later!" didn't seem like a good counterpoint to me.
The way Rose thinks is quite similar to real-life conservationism, who are justified in that action now will be easier than action in the future. For instance, the sooner there are efforts to save a species from going into extinction, the more manageable it would be. Compare the prompt action taken for the California Condor, who have made a recent rebound in wild population, to the Passenger Pigeon, a once-abundant species that went extinct because any major action taken was too late, as everyone was convinced the pigeons would never completely go away.
Rose is definitely rather extreme about it though. A better argument would be, "We have a thousand years to come up with a solution for it. You should take the time to find the best possible solution, then work on it to the best of your abilities so it can be the best answer you can possibly make," which is how those conservation efforts are actually planned out. (Not thinking things through was how efforts to stave off extinction of the Giant Panda only decreased their numbers further; people didn't realize how easily stressed they were around humans.)