Even though academic research is often viewed as the preferred career path for PhD trained scientists, most U.S. graduates enter careers in industry, government, or "alternative careers." There has been a growing concern that these career patterns reflect fundamental imbalances between the supply of scientists seeking academic positions and the availability of such positions. However, while government statistics provide insights into realized career transitions, there is little systematic data on scientists' career preferences and thus on the degree to which there is a mismatch between observed career paths and scientists' preferences. Moreover, we lack systematic evidence whether career preferences adjust over the course of the PhD training and to what extent advisors exacerbate imbalances by encouraging their students to pursue academic positions. Based on a national survey of PhD students at tier-one U.S. institutions, we provide insights into the career preferences of junior scientists across the life sciences, physics, and chemistry. We also show that the attractiveness of academic careers decreases significantly over the course of the PhD program, despite the fact that advisors strongly encourage academic careers over non-academic careers. Our data provide an empirical basis for common concerns regarding labor market imbalances. Our results also suggest the need for mechanisms that provide PhD applicants with information that allows them to carefully weigh the costs and benefits of pursuing a PhD, as well as for mechanisms that complement the job market advice advisors give to their current students.