That is the literal first paragraph of the US constitution. I cannot imagine a valid legalistic argument that ignores that. When first establishing the constitution, it also didn't appear in a vacuum, the pre-existing states and confederation were already democratic for some time. So all authority/validity/legitimacy the US constitution has comes from the population, back then. And through continuing use, participation and broad acceptance until present.
And of course, as a practical matter in a representative democracy, between elections, the people do have far less of an influence. They can basically only voice their opinions, threaten to vote differently in the next election, or start a revolution. But that doesn't absolve them of their responsibility on election day.