Even some conservatives support a national carbon price, but it's unlikely with this Congress.
It's not surprising that California has asked the country to tax carbon pollution. You may also have heard the Rex Tillerson, incoming secretary of state, supports a price on carbon; the weight behind his declarations is questionable, but the National Review sees him as positively green. Elon Musk, friend of Peter Thiel, also promotes the policy.
But while think-tank Republicans propose swapping corporate taxes for a carbon price, the reality is that most Republicans are bound by pledges not to add new taxes.