Amendment 12 to the U.S. Constitution, ratified in 1804, providing for election of the president and vice president by the electoral college: should there be no majority vote for one person, the House of Representatives (one vote per state) chooses the president and the Senate the vice president.
If the states give their electoral votes to the nationwide winner then there will always be someone reaching 270 EC votes thus the House will never be required to elect the president.
I know it hasn't happened since 1824. "As no presidential candidate received a majority of electoral votes in the election of 1824, the U.S. House of Representatives votes to elect John Quincy Adams, who won fewer votes than Andrew Jackson in the popular election, as president of the United States" that does not negate the fact that this drive would take away some of congress's authority.