Saying the economy is a cover for the elites to manipulate the masses is like saying sex is just something advertisers made up to sell beer. They are taking advantage of a situation, they didn't create the situation.
The fact is that a carbon tax would be a new line item on the everyman's bill. It's fewer dollars in their pockets to go out and spend on all the things they want. Less consumer spending means lower employment, more foreclosures, higher debt, increased demand on public services, etc. All things people legitimately don't want. Even if it is for a good cause, our style of democracy makes such a proposal political suicide, even before elites start throwing their weight around.
And frankly, even the elites are mere pawns of the economy. The Koch family did not use their power to make oil profitable, the profitability of oil made the Koch family powerful. If someone finds a way to make solar panels print money better than oil wells then Big Solar is going to be able to outspend Big Oil on all these climate change PR campaigns. The smart elites on the side of Big Oil will switch over to the more profitable team while the dumb ones lose their elite status along with their wealth as they go down with a sinking ship. Being enthralled by people selected by the invisible hand is just being controlled by the invisible hand with an extra step.
There's no such thing; anthropomorphizing “the economy” — which is an arbitrary abstraction and any measure of its health is even more arbitrary — is just a cover for protecting the interests of particular elites; economic concerns are prioritized as essential to the degree they are key interests of the relevant elites.
A government that acts this way isn't a pawn of the invisible hand of the market, but of the hand (often quite visible if you don’t get taken in by the “the economy” misdirection) of the people with cozy personal and business relationships with politicians.