President Barack Obama will lay out his plan for reducing the nation's deficit Wednesday, belatedly entering a fight over the nation's long-term financial future. But in addition to suggesting cuts—the current focus of debate—the White House looks set to aim its firepower on a more divisive topic: taxes.

In a speech Wednesday, Mr. Obama will propose cuts to entitlement programs, including Medicare and Medicaid, and changes to Social Security, a discussion he has largely left to Democrats and Republicans in Congress. He also...