In her first conversation with Winterbourne, Daisy hyperbolically describes Europe as "nothing but hotels." With this comment, she presents her position as a tourist as something that is absolute; in other words, she thinks her perspective is universal.
Although Daisy knows that Europe doesn't actually solely consist of hotels, she isn't interested in assuming the vantage point of a local. She probably recognizes that Europe seems to be nothing but hotels because she is moving from hotel to hotel. Nevertheless, she doesn't care to distinguish her individual experience of her surroundings from how other people experience them. Unlike Winterbourne and other American expatriates, who put sustained effort into masking their foreignness, Daisy has no fear of acknowledging that she's an outsider.
Daisy's remark may be articulated as a complaint, but the narrator notes—through Winterbourne's perspective—that she doesn't make it "with a querulous accent." In fact, she goes on to explain that the hotels are "very good" and that Europe is "perfectly sweet." This shows that she not only perceives Europe through the eyes of a temporary visitor, but that she is pleased to see Europe this way.
Randolph and Daisy both frequently employ hyperbole in their dialogue, which contributes to the stereotype of American overindulgence. Although Daisy's hyperbole is intentional, it nevertheless provides insight into her limited perception. She doesn't seem to notice anything beyond what is offered to her on the surface. The age-old sophistication that other Americans seem to see in Europe doesn't affect Daisy. She's content with occupying the position of foreigner, and therefore doesn't seek to escape it.
At the start of Part 2, Daisy recounts her family's time in Rome to Winterbourne. She hyperbolically adds that they'll stay through the winter unless they catch the fever and die. This comment, though taken as mere hyperbole at this point in the narrative, foreshadows her death at the end of the novella.
We are going to stay all winter, if we don’t die of the fever; and I guess we’ll stay then.
The remark Daisy makes to Winterbourne seems, on the surface, to be a characteristic instance of heedless, juvenile hyperbole. Daisy frequently exaggerates to make light of people's concerns for her. Before she leaves with Winterbourne, both her mother and Mrs. Walker warn her that going "at this unhealthy hour" is a bad idea. In her conversation with Winterbourne, Daisy refers back to their concerns with the intention of trivializing them, making them seem overly concerned and worried about her health. In doing so, she emphasizes her own carefree spirit.
At this point, the reader merely takes this as one of Daisy's many characteristically brazen statements. Little do Daisy and the reader yet realize, though, that she is foreshadowing a very real outcome.