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.