Read the Constitution. When it refers to *citizens* it uses that term. When it refers to *the people*, it is referring to everyone living within the US, regardless of whether they are citizens or not. (Even the folks living here illegally are counted among "the people".)
Article I, Section 2: The House of Representatives shall be composed of Members chosen every second Year by the People of the several States,. . .
Hmmm... Foreign residents are not supposed to be able to vote; whether or not they actually do is another discussion altogether. Interestingly, the above quote, and the preamble "We the people of the United States of America," are the only two uses of the word "people" in the text of the Constitution. Citizen is used eleven times, mostly as regards elegibility for office.
The Bill of Rights uses "the people" five times, and "citizen" exactly zero times. The two documents were authored by different people. (The individual doing the original draft, that is. Many of the same people were involved in ratifying both.) It is entirely possible that "the people" was a stylistic term rather than differentiating between citizen and non-citizen. The Tenth Ammendment reads, "The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people." From this use of the word, one could argue that, as power over a country is not usually held by non-citizens, "the people" referrs to the citizenship.
Also, note the consistant use of the word "the" preceeding the word "people," which implys a specific group of people (citizens of the United States) not just any random set.
Now, where the documents use the word "a person", it is much more literally any person, citizen or not, given that several instances first mention "a person" or "no person", and then modifiy by specifying a length (or status) of citizenship. In the Bill of Rights, the word "person" appears in the fourth and fifth ammendments, and is in regard to search warrents and court procedures.
Now, before somebody starts citing supreme court cases, I am sure that the courts have probably held different interpretations. The above is mine, and I make no claim otherwise.