The most significant proponent of NASA funding has been Neil deGrasse Tyson. A key argument that Tyson makes is the positive externalities that result from NASA because of the way it combines human imagination with powerful scientific tools. In an educational climate where the U.S. consistently fails to produce enough quality STEM workers, an argument to inspire a passion for science should not be ignored. However, there is another argument that gets overlooked far too often is the role of government in research and innovation.
A popular axiom these days seems to be that government can't do innovation and only the free market can produce the type of innovation that increase growth and welfare. The market can indeed be a powerful force but can sometimes be limited by the profit motive. "Businesses will invest in solar whenever it becomes profitable/competitive" or something similar is a phrase I have heard when discussing the need for "green" energy sources. A major problem with this type of reasoning is the dismissal of the path that technology takes to become profitable. The Department of Energy states that they have invested $1 billion since 1995 in solar technology to increase its efficiency and reduce costs. Government funded research has helped to raise solar energy to a competitive level with fossil fuel technology.
Noah Smith wrote a post about why libertarians should support solar energy demonstrating the ways it can decentralize the production of energy. In the post, he also mentions that government funded basic research is a better use of funds than private subsidies to solar companies. This point is an important one because it describes how the government can augment markets instead of the classic claims of interference. By funding basic research, the government can speed up the progression of technologies like solar energy which have enormous social benefits. Without basic research, it is likely that solar technology would have taken much longer to reach its currently level of competitiveness. A similar story can be spun for the progression of the internet. Many will balk at claims about the importance of government in the development of the internet, such as Andrew Morriss in an article written 15 years ago (produced from a quick Google search). However, the vital portion of the internet's narrative is the basic research that the government funded, which eventually led to the internet as we know it. Basic research can get technologies to a level of effectiveness that allows market forces to use them in the most productive way.
The argument for basic research is a phenomenal argument for the funding of NASA. NASA is a place where intensely passionate and intelligent individuals wrestle with problems beyond the scope of everyday life. Along the way, the discoveries made by NASA tend to have very tangible benefits for society. Here is a link to NASA's innovation page where anyone can see the social application of the findings of the organization's scientists.
It is alluring for politicians and taxpayers to cut funding for basic research and programs like NASA because it is a long-term investment in a political world dominated by short-term, electoral logic. The funding of social welfare programs understandably dominates U.S. budgetary discussions and coverage, but the funding of basic research is one of the few areas where the government can effectively invest in the future welfare of its citizens.