There is a way to bypass the Electoral College without a constitutional ammendment. [View all]

[Statistical]

http://www.fairvote.org/national_popular_vote

States are allowed under the Constitution to award their electors however they like. In theory having a coin flip would be legal. The national popular vote is an interstate compact where the states pass legislation to award all their electors to the winner of the national popular vote.

So far 11 states (well 10 states + DC) totaling 165 electoral votes have passed this compact in their state. States which have already passed the national popular vote:
CA
DC
HI
IL
MA
MD
NJ
NY
RI
VT
WA

To avoid penalizing states which adopt early the compact only takes effect once states totaling 270 electoral votes pass similar legislation. Once that happens the winner of the national popular vote will always have 270+ EV and the electoral college is essentially moot. It will still exist until repealed by an amendment but it will be easier to repeal it after a couple of decades under the national popular vote. Even if you are in favor of a full repeal the national popular vote is a way to get there.