Essentially, it's an expression of his nihilism. We tend to think of the "American Dream" in terms of helping others, supporting Truth, Justice, and the American way. But fears such as the Cold War mean that the majority of citizens support the government in squashing those who speak against the current regime.
To borrow one explanation of the quote:
The unintended consequence of liberty is that eventually society becomes so free that even the slightest infringement on liberty is seen as an aggregious (sic) affront to freedom. Machiavelli knew that the only way one could avoid civil unrest entirely was to repress the people. The American Dream, the idea that democracy and a sovereign people is realized in a society, means that unrest will eventually foment, even for the stupidest reasons. The freer we are to allow human nature to surface, the uglier it manifests.
Another interesting interpretation is that The Comedian is referring to the older meaning of "The American Dream", that of the self-made man, that anyone can work their way up to their full potential. The Comedian is a self-made man. He's not superhuman. His origins seem to be humble. And yet, now he is a hero, someone who wields great power. In that aspect, The Comedian is a dark example of the self-made man, someone who has worked their way up to great power over others.
In 1931, James Truslow Adams wrote:
"The American Dream is that dream of a land in which life should be better and richer and fuller for everyone, with opportunity for each according to ability or achievement. It is a difficult dream for the European upper classes to interpret adequately, and too many of us ourselves have grown weary and mistrustful of it. It is not a dream of motor cars and high wages merely, but a dream of social order in which each man and each woman shall be able to attain to the fullest stature of which they are innately capable, and be recognized by others for what they are, regardless of the fortuitous circumstances of birth or position."
Thomas Wolfe said, "…to every man, regardless of his birth, his shining, golden opportunity ….the right to live, to work, to be himself, and to become whatever thing his manhood and his vision can combine to make him."
The Comedian is a self-made man. A horrible one, maybe. But he's made his own choices to get where he was in his world. His eyes were open. Dan is a little bit more of a Martyr-figure. He would have like to have made other choices in life, but didn't.