It would have been helpful if you had cited sources for these quotes, so they could be verified and examined in context. I've been burned by far too many sourceless quotes either turning out to be out of context or, in some cases, actually fabricated. In fact, as we shall see, when examined in actual context, these quotes are far more questionable.
However, first we need to note something important. These quotes are from centuries ago. Languages change. Meanings shift. The word "democracy" in modern times has a more expansive definition than it could have had in the past. Here is Merriam-Webster's definition of democracy (1b) now:
"a government in which the supreme power is vested in the people and exercised by them directly or indirectly through a system of representation usually involving periodically held free elections"
That very much seems to describe the United States, both now and at the start of it! Compare that with the definition of 'democracy' found in Webster's dictionary back in 1828:
"Government by the people; a form of government, in which the supreme power is lodged in the hands of the people collectively, or in which the people exercise the powers of legislation. Such was the government of Athens."
Notice how the mention of exercising power indirectly through electors is not mentioned. Here it refers only to what we would now call
direct democracy; that is, rather than elect representatives who then vote on decisions, people vote on all of the decisions themselves. Essentially, if every decision was a public referendum. This is a form of democracy that has really not taken off outside of in some local areas, in large part due to the obvious logistical difficulties of having that many referendums occur.
So we need to keep this in mind. When we see the word "democracy" used in the late 18th/early 19th centuries, it usually is being used to refer specifically to direct democracy. As time went on, democracy gained a more expansive meaning. When one uses "democracy" nowadays it is with implicit reference to indirect democracy, as that is by far the dominant form of it, with direct democracy being limited to some local governments.
This should be sufficient to reject these quotes as proving the United States is not a democracy, as all they would prove, at most, is that it did not qualify according to the 18th/early 19th century definition of the term, but it most certainly does under the modern definition. However, even taking all of that into account, we should note that various quotes we see condemning democracy even back then put qualifications to clarify they are referring to the idea of direct democracy (sometimes called "pure democracy"), indicating that even back then "democracy" could be understood to refer to indirect democracy as we have in our current discourse.
With all of that said, let's look at the quotes.
This quote is from
a letter from John Adams to John Taylor. As noted, we must consider the different connotations the term had back then. However, Adams' usage of democracy here is... very odd. His primary argument for this is to appeal to the deaths caused by the government after the French Revolution. But the French Revolution established a republic of elected officials! If one is going to declare
that is a democracy, it would seem that the United States should also qualify.
Maybe there's some greater context to the letter that would clarify it. But due to the oddity of the argument when read in a vacuum, and the aforementioned notes regarding definitions, I would not really think this quote really works out that well as proof of the claim being raised.
Moving on:
This is from
The Federalist 10.
As is unfortunately often the case of when an ellipsis is used, important information is being kept out of the quote. The preceding word is "such." Wait, "such democracies"? What are these "such democracies"? The usage of "such" clearly shows we're talking about a specific form, not necessarily all democracies. So let's take a larger look at the paragraph the quote is from:
"From this view of the subject it may be concluded that a pure democracy, by which I mean a society consisting of a small number of citizens, who assemble and administer the government in person, can admit of no cure for the mischiefs of faction. A common passion or interest will, in almost every case, be felt by a majority of the whole; a communication and concert result from the form of government itself; and there is nothing to check the inducements to sacrifice the weaker party or an obnoxious individual. Hence it is that such democracies have ever been spectacles of turbulence and contention; have ever been found incompatible with personal security or the rights of property; and have in general been as short in their lives as they have been violent in their deaths."
Madison here is referring to a "pure" democracy, i.e. absolute direct rule by the citizens; this was what we discussed as being a direct democracy earlier. In his next paragraph he starts contrasting it with a republic. Thus to try to claim this as some kind of indictment of "democracy" when it's referring specifically to direct or pure democracy, is erroneous. As I noted before, even back then some felt it necessary to qualify the term "democracy" to demonstrate the specific form they were discussing, as Madison does here.
It's no wonder the citation isn't given, because this is a very questionable one. You see, this comes from the constitutional debates... but those were not transcribed exactly word for word. Instead we are left with notes given by people who were there, which were obviously frequently paraphrased so they'd be able to actually write it down. There are actually three accounts of Hamilton's speech in question, and only one of them has that quote. You can see it all
here. The main part of the page is from James Madison's notes of the convention (which are usually considered the closest thing we have to an "official" record), and the quote is not there, nor is democracy mentioned. In a footnote it mentions how two other people recorded Hamilton's speech; one of them has the quote, and the other does not. The second does mention democracy, but unfortunately it so scattered in its reporting it's hard to make much sense of. Due to the circumstances of the record, the authenticity of the quote is highly suspect.
Of the quotes, we have (in opposite order) one that may not even be real, one that confines its attacks to "pure democracy", and one that, while admittedly decrying the problems of democracy, uses as an example an elected republic!
Furthermore, to say that John Adams "came up with the Constitution" seems rather erroneous when one considers he was not at the constitutional convention--in fact, he was over in
Britain at the time. He exerted an indirect effect in that he wrote the Massachusetts constitution, which was an influence, but to say he "came up with the Constitution" is simply false because he was off in Britain when they were doing that.