A carbon tax is widely accepted as the most effective policy for curbing carbon emissions but is controversial because it imposes costs on consumers. An alternative, `nudge,' approach promises smaller benefits but with much lower costs. However, nudges aimed at reducing carbon emissions could have a pernicious indirect effect if they offer the promise of a `quick fix' and thereby undermine support for policies of greater impact. Across six experiments, including one conducted with individuals involved in policymaking, we show that introducing a green energy default nudge diminishes support for a carbon tax. We propose that nudges decrease support for substantive policies by providing false hope that problems can be tackled without imposing considerable costs. Consistent with this account, we show that by minimizing the perceived economic cost of the tax and disclosing the small impact of the nudge, eliminates crowding-out without diminishing support for the nudge.