President Obama claimed credit on Tuesday for an improving economy and defiantly told his Republican adversaries in Congress to “turn the page” by supporting an expensive domestic agenda aimed at improving the fortunes of the middle class.

Released from the political constraints of a sagging economy, overseas wars and elections, Mr. Obama declared in his sixth State of the Union address that “the shadow of crisis has passed,” and he vowed to use his final two years in office fighting for programs that had taken a back seat.

He called on Congress to make community college free for most students, enhance tax credits for education and child care, and impose new taxes and fees on high-income earners and large financial institutions.