Given that the US has been so slow to come to the party to even think of seriously addressing climate change it seems almost hypocritical of it to threaten retaliatory tariffs on Chinese carbon intensive exports if China does not adequately price carbon. Europe had already threatened to do the same to the US when Europe alone was pricing its carbon emissions. The move might force China to comply - I have written a paper analysing such outcomes in a cut-and-dried game theory setting. The motivation is that by pricing carbon China then gets to collect the duties not the US. Factors working against such an outcome are the abysmally low levels of energy consumption in a country plagued by extremes of climate and a country which is still distant from middle income status.
I prefer the Garnaut approach - tell China to cut its emissions growth to one half its GDP growth rate - not difficult at present - and then target rates of carbon emissions that converge to global uniformity by 2050. Seems fairer given China's situation and more likely to be something China accepts. China is already screaming 'protectionism' in relation to the US and vaguely suggesting a challenge at the WTO. They are suggesting that destination accounting should prevail (customers not producers pay carbon taxes) with US consumers of Chinese carbon intensive goods being held to account. That is, of course, exactly what the US sees itself doing.
What is really to be feared is that attempts to clean up greenhouse gas emissions will become lost in beggar-thy-neighbour protectionism and a world trade war.