The tax could have a negative impact on the working poor, at least initially, but it's important to distinguish between short-term and long-term.
A historical example comes to mind: the collapse of the slave industry in the American South in the 1800s. (Please note that I'm referring to very specific aspects of the trade; I'm not by any means equating slavery with the energy sector, morally or otherwise.)
If you were to consider abolition from a short-term point of view, as many Americans did, it seemed like a terrible idea. It had catastrophic effects on millions of working, poor Americans. After all, it meant crippling the nation's single largest industry.
And yet, when we reflect on the American slave trade and its eventual decline, those hardships are trumped by greater moral and economic imperatives. The moral imperatives go without saying. The economic ones had to do with recognizing the true cost of labor and finding new opportunities, some of which were outside of agriculture.
Some moral and economic imperatives exist in our current conversation about restructuring the energy industry, which are only visible from a long-term perspective. For example, we're morally bound to address the long-term environmental impact and dangerousness of car travel (although, again, I'm not suggesting this moral imperative is equal to that of abolishing slavery). From an economic standpoint, we're also bound to recognize that our current methods of producing and consuming energy are unsustainable.
TL;DR: Sometimes radically restructuring an industry is the smart - and right - thing to do, despite the relatively short-term economic hardships that it causes.