Immigration affects natives through both labor markets and public budgets, yet these channels are usually studied separately. We combine them in a general-equilibrium model with search-and-matching frictions, skill-specific progressive labor taxes, capital taxation and public goods, calibrated to 17 OECD countries over 2015-2019. The welfare effect on natives of a one-percentage-point increase in immigrant inflows varies in sign and size across countries, hinging on immigrants' skill mix, immigrant-native wage gaps, resident unemployment, and tax progressivity. For inflows matching the skill composition of 2019-2024 arrivals, native welfare rises in 14 of 17 economies, and in most cases both skill groups gain, through different channels. Lower-skilled natives gain mainly from higher pre-tax earnings, driven by job creation and complementarity with skilled immigrants; higher-skilled natives gain mainly from lower labor-tax burdens. Evaluating immigration policy thus requires modeling labor-market and fiscal channels jointly: either channel alone gives an incomplete picture of who gains and why.