There is widespread concern that the United States faces a problem in maintaining its position as the scientific and technological leader in the world and that loss of leadership threatens future economic well-being and national security. Business, science, and education groups have issued reports that highlight the value to the country of leadership in science and technology. Is there a real problem in the job market for scientists and engineers today? If so, what sort of policies might resolve the problem? This paper argues that the country's problem in the science and engineering job market differs greatly from a classical labor market shortage. The problem is twofold: inadequate investment in R&D for the economic and security well-being of the country, which keeps earnings and opportunities in science and engineering occupations those that would attract large numbers of young Americans from competing occupations; and unlimited access to immigrant scientists and engineers, who can fill demands at going wages. As long as the United States enjoys an ample supply of immigrant scientists and engineers, it cannot have a classic labor market shortage. The worst it can have is an imbalance between the supply of citizens and immigrants. The author presents a policy--increasing the number and value of graduate fellowships in science and engineering--that can augment the supply of U.S. students in science and engineering without impairing access to immigrant scientists and engineers, and he gives the evidence that this policy would work. If the United States increases research spending, as laid out in the American Competitiveness Initiative and other proposals, and if the nation takes steps to improve the career opportunities for young scientists and engineers, the expanded fellowship policy would help solve the science and engineering workforce issues that have produced the outpouring of concerns documented in this paper. (Contains 10 exhibits and 15 footnotes.)