He was arguing that the all the important and fundamental laws of physics had been discovered. And so all that remained was to work out what was causing perturbations at increasingly esoteric degrees of precision. In other words that the future of science rested on refining previous discoveries, instead of the discovery of new revolutionary concepts. In the words of our OP here that, "all the science that is possible to do "at home" [is] already done."
Yet of course he made these comments just before physics would be completely revolutionized, and rapidly lead to revolutions in life as we know it. This was prior to relativity, prior to quantum mechanics, even prior to atomic models. The thing that makes it utterly ironic is making such comments at such a time after being an inadvertent key player in the discoveries to come.