How does the 12th amendment change how the president and vice president are elected?

The 12th amendment points out that if there is no majority vote by the electoral college, Congress breaks the tie and chooses who wins. In this case, the House of Representatives chooses president with one vote for each state, and the Senate chooses vice president. It makes a big difference between who wins and who loses. It would be a tight race and it would depend on how Congress thinks about the presidential candidates. That's how they'd break the tie.