Their budget is determined by the elected representatives in congress, and influenced by the executive branch.
As a percentage of the national budget, NASA's funding is half of what it was twenty years ago (and dropping), and 1/9th of the peak 20th century value. There is a historical precedent for NASA receiving a much greater degree of federal funding, which would certainly increase the number of active projects and possibly increase the rate at which we gain an interplanetary foothold.
If you want to influence a congressman to make him think that he will get more votes then you should direct the emails directly at that congressman.
"The White House Office of Science and Technology Policy is planning ahead — way ahead. The agency wants you to email ideas for how "the Administration, the private sector, philanthropists, the research community and storytellers" can develop "massless" space exploration and a robust civilization beyond Earth."
This is beautiful.
"We are running out of adventures [...] the mountains have all been climbed, the continents explored, and the romance of sailing away on a tall ship to undiscovered islands is no more. What will fire the imaginations of the next generation?"
http://io9.com/white-house-seeks-advice-on-bootstrapping-a-solar-syst-1647619795