So I'm no climate change denier. I was the energy economist for CEA for the past year. And the chapter I wrote for the Economic Report of the President even obliquely advocates a higher gasoline tax (Mankiw saw through the political phrasing right away)
But honestly, economists are a little bit dogmatic when it comes to advocating a carbon tax or gasoline tax. It is almost a matter of faith, rather than evidence.
If you read the literature on the social cost of carbon, most (including the ipcc) pick an optimal price of carbon of around $14/ton CO2. (And as an aside, in general the studies that find such a value, do not find values statistically different than $0/ton CO2.)
So first, we are ignoring statistics to advocate a positive carbon tax.
And second, we are having faith that such a tax will yield new technology.
$14/ton CO2 is only about 14 cents per gallon of gasoline (1/3 of the current tax on gasoline). Prices of gasoline have increased several hundred cents. Unlikely that that additional 14 cents will have a huge impact on innovation there.
$14/ton CO2 is about 1-2 cents per kWh of electricity (the EPA expects that most ghg reductions would come from this sector).
Yet it is less than the 2 cents tax credit we already give to non-fossil electricity generation. So by that argument, we have already overshot. A tax on carbon would over substitute toward non fossil fuels.
Europe has substantially higher taxes/subsides on carbon already (well beyond what most economists consider optimal; we're talking 3 or 4 times too high) that should be more than enough to spur innovation. It hasn't. Not clear how creating more dead weight loss from an inefficient tax in US would help.
Despite all this you could still argue in favor of a carbon tax. But you should be cognizant that there is little economic evidence to back you up.