We estimate the total dust input from the cool evolved stars in the Small Magellanic Cloud, using the 8 μm excess emission as a proxy for the dust-production rate (DPR). We find that asymptotic giant branch (AGB) and red supergiant (RSG) stars produce (8.6-9.5) × 10^-7 M _⊙ yr^-1 of dust, depending on the fraction of far-infrared sources that belong to the evolved star population (with 10%-50% uncertainty in individual DPRs). RSGs contribute the least (<4%), while carbon-rich AGB stars (especially the so-called extreme AGB stars) account for 87%-89% of the total dust input from cool evolved stars. We also estimate the dust input from hot stars and supernovae (SNe), and find that if SNe produce 10^-3 M _⊙ of dust each, then the total SN dust input and AGB input are roughly equivalent. We consider several scenarios of SN dust production and destruction and find that the interstellar medium (ISM) dust can be accounted for solely by stellar sources if all SNe produce dust in the quantities seen around the dustiest examples and if most SNe explode in dense regions where much of the ISM dust is shielded from the shocks. We find that AGB stars contribute only 2.1% of the ISM dust. Without a net positive contribution from SNe to the dust budget, this suggests that dust must grow in the ISM or be formed by another unknown mechanism.