(And since emissions are not distributed linearly, the losers from a cost-neutral carbon-tax with per-capita-dividend will always be a minority.)
From what I'm being told, fundamental changes need to occur in our consumption to have a measurable impact on climate change. That won't happen with normal people continuing to consume at the same rates they have.
Could a carbon tax be designed such that normal people are effectively reimbursed and heavy emitters pay more? Yes. But you're not going to measurably impact climate change without somehow incentivizing people to use less. At some point, people need to use less, and when you force them to (through taxes or restrictions), it won't be popular politically.