Which Enlightenment idea is expressed in this excerpt from the Declaration of Independence?

The idea that the government should care for and protect its people.

You didn't provide the excerpte, but the Declaration of Independence's strong overall theme is that people are born with natural rights.

Perhaps the most memorable phrase from the Declaration is this: "We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness."

It is also the case that the Declaration of Independence supports the idea that government's power should be determined by the people. The very next words in the Declaration assert, "To secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed."

The founding fathers of the United States had adopted ideas about natural rights and the people's sovereignty from Enlightenment philosophers like John Locke (of England) and Baron de Montesquieu (of France).