Here are two of the points he makes, from the Huffington Post:
2. Carbon tariffs could ignite a green trade war and harm the U.S. economy. China and India have called U.S. proposals for a carbon tariff unacceptable and protectionist and have hinted at retaliation. Developing countries have pointed to U.S. per capita CO2 emissions, which are dramatically higher than the world average, as a basis for retaliating against any U.S. efforts to place tariffs on foreign goods. ...
3. Carbon tariffs are likely to violate global trade rules. While Mr. Krugman correctly notes that global rules provide for the use of trade measures to address environmental issues, they also require that "a connection must be established between the stated goal of the climate change policy and the border measure at issue" and that "the measure must not constitute a means of arbitrary or unjustifiable discrimination" or a "disguised restriction on international trade." It turns out that it is difficult to design a border measure in a way that satisfies these criteria, particularly when you leave it to politicians. As Jeffrey Frankel of Harvard University has written, "border measures to address leakage need not necessarily violate the WTO or sensible trade principles, but there is a very great danger that in practice they will."
His first point makes me wonder the following. The general idea behind carbon tariffs is for developed countries to tax imports from countries which have not taken sufficient steps to fight climate change. In practice, the countries being targeted are India and China (and the U.S., if it does not take action soon). But if, as he points out, developing countries have much lower per capita CO2 emissions, could they just respond with their own carbon tariffs, based on the argument that those producing most of the emissions have not done enough to reduce those emissions?