Not exactly. The original governing document of the United States was the Articles of Confederation and Perpetual Union. The states had far more authority than the central government and Congress. The system of powerful states didn't work. The states couldn't work together and the Congress didn't have authority to settle disputes. By 1788 the Constitution replaced it, which took much power out of state control.
However, there was a lot of suspicion of elections and voting. Remember only white land owning men could vote. Still, there was a fear of the common man highjacking the government.
The Electoral College was built into the Constitution to avoid direct election of the President. Originally the US Senate was not directly elected either. However the US House of Representatives were. Article 1 Sec 2 of the US Constitution states: "The House of Representatives shall be composed of Members chosen every second Year by the People of the several States, and the Electors in each State shall have the Qualifications requisite for Electors of the most numerous Branch of the State Legislature." So essentially if you were able to vote in a state Legislature election, you could vote for the US House Rep too. Again this was a small minority of people in each state, generally wealthy, white males.