Yes.

US Constitution, Article 1, Section 2, is at http://constitution.findlaw.com/article1.html#1.2 . "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.", and the final clause removes some wiggle room. The language is pretty precise, like how it specifies that senators shall be "chosen by the Legislature thereof", but for presidential electors, "Each State shall appoint, in such Manner as the Legislature thereof may direct, a Number of Electors".

Federalist Paper number 52 at http://avalon.law.yale.edu/18th_century/fed52.asp goes into some detail about what Madison or Hamilton was assuming or believing, or at least saying. I see no sign that they contemplated any intermediate electors, and to the contrary, they talk about it in terms like "it is particularly essential that the branch of it under consideration should have an immediate dependence on ... the people".

Now, that doesn't mean that they elected members with first-past-the-post in districts like today. That districting requirement came only in the 1840s. Some were single statewide tickets. Some were districted but statewide (weird). Some had a requirement of majority votes, requiring run-offs. Still, so far as I have determined, they were all elected by the people.