FROM the standpoint of public support, the United States space program faces trouble that a successful shuttle launch on Thursday might only partly reduce. Surveys indicate that the public favors the space program in the abstract, and even specific projects such as the space station or a trip to Mars. But it is unwilling to spend large additional sums of money for space. A significant plurality feels NASA's budget should remain about where it is now - which in effect means a cut as inflation whittles away at a constant amount of funding. When that plurality is combined with those who would cut the space budget, a majority emerges for at best a holding action on space spending. When it comes to spending more tax dollars, the public ranks the space program below the environment, health, education, crime, and drugs; in each of these other areas, a clear majority feels Washington needs to spend more. This does not augur well for the major ``next steps'' in US space efforts, such as moon bases or a trip to Mars. Public support - measured by its willingness to spend more money - will not rise significantly until political leaders do more than stand on the podium at the Johnson Space Center and voice support for big-ticket projects. They must consistently remind the public of practical reasons - such as gathering vital information to guide global environmental protection strategies - to embrace the broader vision of the space program.