President Barack Obama is expected to detail an ambitious domestic agenda in his State of the Union address Tuesday, including measures on immigration, gun control, climate change and education.

The speech will open a limited window for Mr. Obama to accomplish his objectives before the politics of the 2014 and 2016 contests overtake his term. Complicating matters, the address comes as the threat of spending cuts known as the sequester dominate the discussion in Washington. Usually, a president delivers the speech in tandem...