The proof might boil down to just two words: two degrees. An early statement at Doha that America remains committed to the global goal of limiting warming to 2C above pre-industrial levels would be a clear sign.
Every statement from US diplomats at the Doha negotiations will be closely scrutinised for signs that Obama will indeed make climate change a priority of his second term – and that America remains committed to the global agreement diplomats have been seeking for 20 years.
Campaigners say Obama's re-election, superstorm Sandy and New York City mayor Michael Bloomberg's endorsement – predicated on climate change – put climate change back on the domestic agenda.
Opinion polls suggest public concern in the US about climate change was rising even before Sandy. Campaigners argue Obama needs to engage on climate, if he wants to safeguard his legacy as president.
"President Obama's re-election provides him with an opportunity to seal his legacy as a truly transformative leader, but he needs to address climate change," said Andrew Steer, president of the World Resources Institute
"I think history will judge any president from now onwards not to have succeeded if he doesn't really grapple with this issue seriously."