We explore the depletion attractions that arise between hard colloidal spheres immersed in a nonadsorbing polymer solution of DNA. We spatially confine two 1.25 mu m silica spheres in a scanning optical tweezer and quantitatively examine their interaction potential in double-stranded DNA solutions of different concentrations. The potentials obtained display variations in depth and range that are consistent with scaling behavior expected for semiflexible polymers near the theta-point. In particular, we clearly observe the crossover from a dilute solution of Gaussian coils to the weakly fluctuating semidilute regime dominated by two-point collisions (Schaefer, D. W.; Joanny, J. F.; Pincus, P. Macromolecules 1980, 13, 1280-1289). We also quantitatively test the Asakura-Oosawa model for these systems and show that it may be used in both the semidilute as well as the dilute regime. At fixed DNA concentration, we find that the range and depth of the interparticle potentials do not change significantly for ionic concentrations between 1 and 50 mM.