If the US President was elected by the House of Representatives would you still support the Electoral College?

This has not happened since 1824, once before in 1800, but if the winner of the popular vote losing (1824, 1876, 1888, 2000) and the electoral college not reflecting the closest of the popular vote couldn't do it. Well in 1968 (popular vote Nixon wins by 500,000 votes but wins the Electoral College 301 to 191, 46). This lead to a proposed amendment to have run-off elections failed in the Senate due to small states wanting to keep the EC. Would a President Elected the House of Representative be the breaking point for the general American public.