As the battle intensifies over how much authority President Obama has to take executive measures in the face of congressional inaction, two former United States presidents, James Madison and Richard Nixon, provide the frames of reference.

Madison, the architect of the United States Constitution in the late 18th century, envisioned recurring tension between the executive and legislative branches. Nixon, the first president driven from office by the fear of impeachment, demonstrated what abuse of executive power looks like.

The Republican-controlled House is planning to sue Mr. Obama for exceeding his executive authority, and threats of impeachment are in the air if the president unilaterally exempts — at least temporarily — more undocumented immigrants from deportation.

“There always is tension with the executive when public policy can’t be made in the legislative process,” said Stephen Wayne, a professor of government at Georgetown University.