In The Great Gatsby Daisy functions as the object of Gatsby's undying affection and absolute obsession. The American Dream is typically associated with home ownership, freedom from other governments, the ability to meet the needs of one's own family or the absolute conquest of wealth.
Although Gatsby used many of these means to get Daisy, their relationship ended up being superficial and purposeless. It was a dream in itself. We see this specifically in chapters 6-7. As Gatsby makes the bold claim that she never loved Tom more than Gatsby, he it speaking with a confidence borne of his ability to now have everything it takes to make her happy, but he had to work years and in an underhanded way to get it. Gatsby may have never pursued the means that he learned from the Codys and the Wolfsheims in his life had it not been for the idea that these were ways to obtain Daisy more quickly.
Here's a quote to use:
"She never loved you, do you hear?" he cried. "She only married you because I was poor and she was tired of waiting for me. It was a terrible mistake, but in her heart she never loved any on except me!"
This is Gatsby speaking to Tom in chapter 7.