Given the nature of the question as one that automatically presumes its importance, it can be understood that Jefferson's writing was powerful and significant to the development of American History. One of the most significant effects of Jefferson's document was that it gave a sense of voice to the Colonial struggle. In many ways, Jefferson's writing helped to articulate the rage and sense of anger that had defined the Colonial cause. Jefferson's writing moved the cause away from the fringe and radical element and moved it to the center. This is substantiated by General Washington reading it to his troops as British vessels amassed in Boston Harbor. At the same time, people in Colonial cities were rallied to action upon hearing the words in Jefferson's document, causing them to riot and display the very anger that the document articulated. In this regard, an argument can be made that one way life in America might have been different without the The Declaration of Independence was in the absence of a codified means of communicating the colonial rage.
One of the byproducts of Jefferson's writing was in its universal appeal. The document moved the struggle of the Colonists from a purely political battle to a moral or ethical one that applied to all human beings. An example of this was how the document was received by people of color in America. Enslaved African- Americans recognized that the call for freedom that Jefferson echoed for the Colonies was something dear to their own hearts. Without the document, many of these individuals who have not volunteered for the Colonial effort and also not understood the vocabulary of freedom that defined their own condition in the New World.
Finally, I think that a case can be made that the document was both a part of the history of the American Revolution, but also transcended it. In later moments in American History such as the drafting of the Constitution, the Civil War, the fight for Women's Rights, and the Civil Rights Movement, the language of the document was appropriated. The legacy of Jefferson's writing was to give voice to all of these political struggles, making them more human than anything else. One can surmise that the absence of the document might have created a vacuum for other movements that sought to authenticate voice and experience. Giving voice to future American social and political movements is another way in which America might have been fundamentally different if there had been no Declaration of Independence.
The Declaration of Independence freed the American colonies from Britain's rule. Without this important document, we would still be dependent on Britain's government, paying taxes that the colonists were obviously opposed to, and living like the British wanted us to live. With the Declaration of Independence, we were allowed to be free and create our own form of government for the people. The United States no has the longest lasting Constitution and we continue to thrive as a nation. This document led to all the successes, and struggles, of our country.