What you are describing is a “democratic republic” – a representative form of government (republic) that gives ultimate power to the citizens (democracy) in the election of officials. Which is also known as representative democracy, which is really a form of republic (hence democratic-republic, with democratic as modifier). A country where people vote directly on issues is stam a democracy, no? And a country where the vote is not distributed equally is a republic that is not democratic. Of course, as is self-evident, the U.S. did not start out as democratic, but now can be described as such.
And stam, the term “federalism” is not really in contradiction of anything. It just means that there is a division between tiers of government – at the local level, and in a central governing power.