The National Popular Vote bill does not "do away with the Electoral College.'

All of the 270+ presidential electors from the enacting states will be supporters of the presidential candidate receiving the most popular votes among all 50 states (and DC)—thereby guaranteeing that candidate with an Electoral College majority.

Now, the Electoral College would not prevent a candidate winning in states with 270 electoral votes from being elected President of the United States 

In 1969, The U.S. House of Representatives voted for a national popular vote by a 338–70 margin.   

Recent and past presidential candidates who supported direct election of the President in the form of a constitutional amendment, before the National Popular Vote bill was introduced: George H.W. Bush (R-TX-1969), Bob Dole (R-KS-1969), Gerald Ford (R-MI-1969),  Richard Nixon (R-CA-1969),