Using first-principles density-functional-based calculations, we study the effect of doping and pressure on the manganese-based pyrochlore compound, Tl2Mn2O7, which exhibits colossal magnetoresistive behavior. The theoretical study is motivated by the counterintuitive experimental observation of suppression of the ferromagnetic transition temperature upon application of pressure and its enhancement upon substitution of Mn by a moderate amount of nonmagnetic Sb ion. We also attempt to resolve the issue related to crystal structure changes that may occur upon application of pressure.