The significance of Daisy's statement is that, in one respect, it implies the superficiality of her character. It is a silly thing for her to say, and she says it for effect, to seem warm and charming. Nick knows he is "not even faintly like a rose," but he recognizes the emotional effect Daisy can create with such a ridiculous statement:
She was only extemporizing but a stirring warmth flowed from her as if her heart was trying to come out to you concealed in one of those breathless, thrilling words.
The key element of Nick's description of Daisy is his use of "as if." Daisy's heart was not reaching out to Nick; she was emotionally dishonest and manipulative.
Daisy's words to Nick, in the context of the chapter, suggest another interpretation. She calls Nick "an absolute rose" immediately after Tom leaves the table after the butler gives him a message. Daisy knows, and Nick soon finds out, that it is Tom's mistress who has interrupted their dinner. Daisy's comment to Nick helps her cover Tom's awkward, sudden departure; it also represents an effort on Daisy's part to make herself feel less alone, less powerful, and more valued in someone eyes, even Nick's.
In my opinion, the statement to which you refer (which can be found in the first chapter of The Great Gatsby), reveals quite a lot about Daisy's character. Before delving further, let's look at the comment in context:
"I love to see you at my table, Nick. You remind me of a--rose, an absolute rose. Doesn't he?" She turned to Miss Baker for confirmation: "An absolute rose?"
This was untrue. I am not even faintly like a rose. She was only extemporizing, but a stirring warmth to you concealed in one of those breathless, thrilling words. Then suddenly she threw her napkin on the table and excused herself and went into the house. (15)
Now, I'm sure Daisy's "rose" statement is open to interpretation, but in my opinion, it shows what a shallow ditz of a gilded flapper Daisy really is. It proves that Daisy (as Gatsby will later confirm) is the voice of inherited money, . . . and not much else. It's also interesting that Nick uses the word "extemporize" to describe Daisy's words. Extemporize, of course, means to do something, particularly to perform or speak without prior planning or thought. Yeah. That would be Daisy. This is the gal who lost it over Gatsby's shirts. Daisy's character is weak and, as a result, most of her statements are weak as well. In fact, even when she tries to be serious, she falters. She tries to convince Tom that she's leaving him by saying, "I am, though." Sad, isn't it?
Thus, I suppose it started with Daisy's "rose" comment when I say that I feel sorry for her. There is no better evidence of how money can corrupt a mind than the character of Daisy Buchanan.