Fortunately, we live in a time where any of us can look over the notes people made at the Constitutional Convention itself.

Some of the various ideas and justifications follow:

Mr. SHERMAN was for the appointment by the Legislature, and for making
him absolutely dependent on that body, as it was the will of that which
was to be executed. An independence of the Executive on the supreme
Legislature, was in his opinion the very essence of tyranny if there was
any such thing.

Mr. WILSON renewed his declarations in favor of an appointment by the
people. He wished to derive not only both branches of the Legislature
from the people, without the intervention of the State Legislatures but
the Executive also; in order to make them as independent as possible of
each other, as well as of the States;

Mr. WILSON made the following motion, to be substituted for the mode
proposed by Mr. Randolph's resolution, "that the Executive Magistracy
shall be elected in the following manner: That the States be divided
into ______ districts: & that the persons qualified to vote in each
district for members of the first branch of the national Legislature
elect ______ members for their respective districts to be electors of
the Executive magistracy, that the said Electors of the Executive
magistracy meet at ______ and they or any ______ of them so met shall
proceed to elect by ballot, but not out of their own body ______ person
in whom the Executive authority of the national Government shall be
vested."

Mr. WILSON repeated his arguments in favor of an election without the
intervention of the States. He supposed too that this mode would produce
more confidence among the people in the first magistrate, than an
election by the national Legislature.

Mr. GERRY, opposed the election by the national legislature. There would
be a constant intrigue kept up for the appointment. The Legislature &
the candidates wd. bargain & play into one another's hands, votes would
be given by the former under promises or expectations from the latter,
of recompensing them by services to members of the Legislature or to [4]
their friends. He liked the principle of Mr. Wilson's motion, but fears
it would alarm & give a handle to the State partisans, as tending to
supersede altogether the State authorities. He thought the Community not
yet ripe for stripping the States of their powers, even such as might
not be requisite for local purposes. He was for waiting till people
should feel more the necessity of it. He seemed to prefer the taking the
suffrages of the States instead of Electors, or letting the Legislatures
nominate, and the electors appoint. He was not clear that the people
ought to act directly even in the choice of electors, being too little
informed of personal characters in large districts, and liable to
deceptions.

Mr. WILLIAMSON could see no advantage in the introduction of Electors
chosen by the people who would stand in the same relation to them as the
State Legislatures, whilst the expedient would be attended with great
trouble and expence

Mr. GERRY, according to previous notice given by him, moved "that the
National Executive should be elected by the Executives of the States
whose proportion of votes should be the same with that allowed to the
States in the election of the Senate." If the appointmt. should be made
by the Natl. Legislature, it would lessen that independence of the
Executive which ought to prevail, would give birth to intrigue and
corruption between the Executive & Legislature previous to the election,
and to partiality in the Executive afterwards to the friends who
promoted him. Some other mode therefore appeared to him necessary.

I cannot find any debate over suffrage until after these discussions.

The antidemocratic sentiment is the Convention was very strong - there was debate on whether even the House should be popularly elected, on the grounds that:

Mr. SHERMAN opposed the election by the people, insisting that it ought
to be by the State Legislatures. The people he said, immediately should
have as little to do as may be about the Government. They want
information and are constantly liable to be misled.

Mr. GERRY. The evils we experience flow from the excess of democracy.
The people do not want virtue, but are the dupes of pretended patriots.
In Massts. it had been fully confirmed by experience that they are daily
misled into the most baneful measures and opinions by the false reports
circulated by designing men, and which no one on the spot can refute.
One principal evil arises from the want of due provision for those
employed in the administration of Governmt. It would seem to be a maxim
of democracy to starve the public servants. He mentioned the popular
clamour in Massts. for the reduction of salaries and the attack made on
that of the Govr. though secured by the spirit of the Constitution
itself. He had he said been too republican heretofore: he was still
however republican, but had been taught by experience the danger of the
levilling spirit.

http://www.nhccs.org/Mnotes.html