There very much is an economy, and people vote based on how they perceive its health. There are certainly elites who have invested quite heavily in convincing people that policies they personally don't want enacted would be unhealthy for the economy, but that is an effect of public policy becoming wholly subsumed by economic concern, not a cause.

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.