A straight-through tax can appeal to conservatives who don't want additional taxes and who dislike taxes that discourage people from working.
We currently tax things – having a job (income tax), creating jobs (corporate tax), owning a home (property tax), and engaging in economic activity (sales tax) – that are good for society. We also tax things that cost society as a whole – alcohol and tobacco and fatty, unhealthy food and environmental degradation. New taxes on carbon emissions can be balanced by reduced taxes on jobs.
A new tax on carbon pollution or gasoline consumption, paired with a cut in the income or payroll tax, creating a revenue-neutral, market-driven solution to an environmental problem while cutting taxes that conservatives dislike.