Early Wednesday morning, as sleep-deprived supporters rallied for a final cheer, President Obama concluded his re-election campaign with a promising glimpse at what the fight was all about: a second-term agenda that can make real progress on issues neglected in the first.

Without question, the president intends to build on and improve the significant accomplishments of the last four years, particularly the full implementation of health care reform and the use of government policy to keep the economy growing. But the president went beyond that in his victory speech and added some less familiar words to his policy vocabulary.

Children should live in a world that is not burdened by debt or weakened by inequality, he said, but also one “that isn’t threatened by the destructive power of a warming planet.” That suggests he knows he has an opportunity to address climate change with more vigor, going beyond auto-mileage standards and renewable-energy jobs to possibly advocating tougher carbon emissions standards.

The president also said he was looking forward to working with Republicans to fix the immigration system, giving him a chance to do more than promote the Dream Act for young immigrants. He could lead the way to comprehensive reform that combines strong enforcement with a path to citizenship for immigrants already here. He also hinted that combating poverty might move higher on his priority list.