The timelines associated with climate change are of an entirely different magnitude from those associated with ordinary politics. The greenhouse gases we emit today will still be affecting the climate in thousands of years, in a time when our current leaders and forms of political organization will have become as obscure as those of the Ancient Greeks are to us now. It is possible that only scholars in under-funded departments will be aware of what the state of global politics looked like in 2010. People with the degrees they issue may worry about how they will find jobs, having specialized in such an obscure and irrelevant field. Quite possibly, the average person will have never heard of Barack Obama, the European Union, the economic resurgence of China, or the existence of Canada.
On the other hand, it is possible that the politics of 2010 will be remembered in the distant future for the same reason the general outlines of Ancient Greek society are remembered now: because they will be seen as an important explanation for why the world is as it has become. In that case, it seems likely that our time will be primarily remembered as the period in history when people could have stopped dangerous climate change, but failed to do so because of their short-sightedness and selfishness.