But now they only campaign in the "swing" states.  With the electoral college a vote in Wyoming has the same weight as 4 votes in California.  This is not the ideal of one person one  vote!  I disagree that the populous states would be more advantaged in a system using the popular vote.  A vote anywhere would be worth the same as anywhere else. 
Having the election work to elect the one with the most votes nationwide would not require a constitutional amendment.  It does not specify the process in detail.  An agreement among electors to vote for the person getting the most votes nationwide would be just a valid constitutionally as the present agreement to vote the winner in each state.  Here is an interesting analysis about the duties of the electors:
http://random-2-cents-worth.blogspot.com/?spref=tw