I agree with much of the first answer, but we have to look to some extent at which people were included in "the people." It is pretty clear that "the people" of the United States who "ordained and established" the Constitution were only those people who were allowed to vote.
In other words, "the people" most clearly did not include women and racial minorities. Depending on who you were at the time, you might have thought that poorer white men were included in "the people." However, the people who were part of setting up the Constitution and in whose name the delegates acted were clearly only white men.
One of the great triumphs of American democracy is the fact that we have moved from this exclusionary view to a much more inclusive view of who "the people" are.
Actually the phrase appears in the Constitution; although Jefferson does comment in the Declaration that the delegates are acting.
in the name, and by the authority of the good people of these colonies
The Constitution speaks of "the People of the United States." It constitutes a deliberate contrast with the opening lines of the Articles of Confederation, which read, "the united States of America in Congress assembled..... Whether the Constitution means the individual citizens or the States themselves comprised of the people has been an issue of intense debate. It is an issue that dogged Constitutional scholars for many years, particularly prior to the Civil War. The argument was, did the Union consist of the individual states who formed it? If so they could easily separate from that Union as the Southern states attempted to do. Or was it a union of the people of the union? If so, individual states had no right to secede. Abraham Lincoln's position from the beginning was that the Union was of the people, and not the states, so the southern States never truly left the Union--they couldn't. It was for this reason when Lincoln planned to reprovision the garrison at Fort Sumter, he wrote not to the Presidency of the Confederacy, which he did not recognize, but to the governor of the State of South Carolina.
The safest and probably most accurate approach would be to interpret the language of the Constitution in its plain and simplest meaning: "the people of the United States," who acted through their chosen delegates. Even the Tea Partiers can't argue with that.