Do you have a better idea how to convey the information about true cost of action to the market? You can't let it assume the cost is 0 like it did for last 200 years.
As others have suggested, a corresponding decrease in income and corporate tax such that you get a revenue neutral framework with no additional wasteful government spending would be supported by many, including those on the right. This may also have an additional effect on neutralizing any downwards economic impact from the carbon taxation.