Question

Governments are instituted among men, deriving their just powers from the consent of the governed. . . . [w]henever any form of government becomes destructive of these ends, it is the right of the people to alter or to abolish it, and to institute new government.1the excerpt most reflects which enlightenment idea?

Answer 1

I believe the answer is popular sovereignty  
popular sovereignty refers to the idea that the highest authority that exist in a nation fall to the hands of the majority of people, not the government.
In this view, government officials (including president) are just someone that people put on their paycheck to do whatever the people demanded them to do.

Answer 2

This excerpt from the third sentence of te declaration of Independence highlighting the inalienable right of the people to alter or to abolish it, and to institute new government' is the hallmark of true democracy.