US emissions in 2008 were 5.8bn tonnes.
The current bill, iirc, has a price limit of $28/tonne CO2.
US GDP is about $14tr
If all the permits were paid for, emissions weren't cut and the money disappeared, then the average cost would be 1.17% of the average American's income.
Of course, some permits will be given away for free, some CO2 emissions will escape permits, many places will cut emissions at a cost far cheaper than $28/tonne and the money will be reinvested and won't disappear.