Space missions to near-Earth objects (NEOs) are being planned at all major space agencies, and recently a manned mission to an NEO was announced as a NASA goal. Efforts to find and select suitable targets (plus backup targets) are severely hampered by our lack of knowledge of the physical properties of dynamically favorable NEOs. In particular, current mission scenarios tend to favor primitive low-albedo objects. For the vast majority of NEOs, the albedo is unknown. Here we report new constraints on the size and albedo of 65 NEOs with rendezvous ∆v <7 km s-1. Our results are based on thermal-IR flux data obtained in the framework of our ongoing (2009-2011) ExploreNEOs survey using NASA's "Warm-Spitzer" space telescope. As of 2010 July 14, we have results for 293 objects in hand (including the 65 low-∆v NEOs presented here); before the end of 2011, we expect to have measured the size and albedo of ~700 NEOs (including probably ~160 low-∆v NEOs). While there are reasons to believe that primitive volatile-rich materials are universally low in albedo, the converse need not be true: the orbital evolution of some dark objects likely has caused them to lose their volatiles by coming too close to the Sun. For all our targets, we give the closest perihelion distance they are likely to have reached (using orbital integrations from Marchi et al. 2009) and corresponding upper limits on the past surface temperature. Low-∆v objects for which both albedo and thermal history may suggest a primitive composition include (162998) 2001 SK162, (68372) 2001 PM9, and (100085) 1992 UY4.