To the framers, the great danger of democratic government is the risk of

The great danger of democratic government to the framers is the rick of the Tyranny of the majority. Democracy is a complicated constitution as it works towards the opinions and desires of the common people but still leaves some people dissatisfied because of the mentioned reason.

That would be the risk of tyranny of the majority.

The Founding Fathers were wary of the tyranny of the majority and the pure direct democracy because there could rise a demagogue who could sway the majority and work only for the benefit of the majority at the expense of the minority. The electorate system and the faithless electors within it is there in order to prevent the tyranny of the majority and also to prevent the possible use of democracy to overthrow democracy.