At its core, a carbon tax is a tax on the carbon content of fossil fuels. It would raise revenue and result in reductions of CO2. Some supporters have pushed for a revenue neutral carbon tax, which would be paired with tax cuts in other areas.
Environmental groups, some corporations, and most economists - even conservative economists -- prefer a carbon tax over regulations. A carbon tax is considered more economically efficient than a cap-and-trade program and a more effective tool to reduce CO2 than emissions caps, like the Clean Power Plan. In addition, a carbon tax is flexible and scalable.
Most politicians - especially Republicans -- strongly oppose a carbon tax. First, some Republicans don't support the underlying premise that carbon emissions need to be reduced. In addition, many Republicans have an intrinsic opposition to any new tax and are dubious about efforts to make it revenue neutral. They oppose the tax because of its potential impact on the energy industry, including possible job losses and a reduction in energy security.
While Democrats are more open to a carbon tax, there is a lack of strong Democratic advocates. Notably, Hillary Clinton has not endorsed it as a part of her energy and environment agenda. Given the lack of political support, a carbon tax is unlikely to be enacted in the near term.