Here is what needs to happen.

Article II Section 1 grants to the states the power to appoint electors to the Electoral College “in such manner as the Legislature thereof may direct”. 

The 14^th Amendment guarantees equal protection of the laws.

State winner-take-all laws violate the 14^th Amendment by disenfranchising all voters who voted for the losing candidate, and may be challenged under the 14^th Amendment as being unconstitutional.

A person from the losing side (say in Florida) can file a federal suit challenging the electors in his/her state as unconstitutional under the 14^th Amendment.

The Supreme Court decides that winner-take-all laws are unconstitutional and electors must be chosen in a manner reflective of the vote in the state (i.e. proportional).

After the states re-appoint their electors in accordance with the Court’s ruling, Clinton wins the Electoral College 260-257 (do the math).

All this needs to happen between Dec 19 when the state electors convene and cast their ballots, and Jan 20, Inauguration Day. 

If the federal courts had enough time to overrule the state of Florida recount in 2000 prior to Inauguration Day, they have enough time to decide this case prior to Inauguration Day.