"How would the sudden increase in energy cost affect poor people?"
Why would it be sudden? Ramp the tax up, say, $1/tonne per year.
"How would the tax affect economic growth and unemployment? It's hard to tell since we haven't done it yet."
Do you imagine the regulation approach would cost less, for the same effect?
"Since it would not be imposed in the rapidly growing economies of China and India, it would also do little to reduce global carbon emissions."
And this distinguishes a US tax from a US regulation how?