Wetted-foam, direct-drive target designs are a path to high-gain experiments on the National Ignition Facility (NIF) [J. Paisner et al., Laser Focus World 30, 75 (1994)]. Wetted-foam designs [S. Skupsky et al., in Inertial Fusion Sciences and Applications 2001, edited by K. Tanaka, D. D. Meyerhofer, and J. Meyer-ter-Vehn (Elsevier, Paris, 2002)] take advantage of the increased laser absorption provided by the higher-atomic-number elements in a target ablator composed of plastic foam saturated with deuterium-tritium (DT). The increased laser coupling allows more fuel to be driven with the same incident laser energy, resulting in increased hydrodynamic stability and target gain. A stability analysis of a 1-MJ design was performed using the two-dimensional hydrodynamic code DRACO [P. B. Radha et al., Phys. Plasmas 12, 032702 (2005)]. Simulations examining the effect of the expected levels of laser nonuniformities (single-beam and multiple-beam) and target nonuniformities (surface and ice roughness) have been performed. A nonuniformity-budget analysis has been constructed and suggests that two-dimensional (2D) smoothing by spectral dispersion (SSD) [S. Skupsky et al., J. Appl. Phys. 66, 3456 (1989)] is needed to reduce single-beam nonuniformities to levels sufficient for ignition to proceed. Two integrated 2D simulations with 0.75-μm initial ice roughness, multiple-beam nonuniformity, surface roughness, and imprint were completed, one with 2D SSD smoothing and one with 1D SSD. The former ignited and produced a gain of 32, while the latter failed to ignite. A third integrated 2D simulation with 1-μm initial ice roughness and an ice power-law spectral index of 1 was also completed and produced a gain of 27.