It's more than a day, I think. Leo sees her, saves her from a suicide attempt, has dinner with her and parties with her the following night, then the night after that is the iceberg. "Titanic" is not even a love story per se. He saves her, they become friends, she sleeps with him to get revenge for her fiance's abuse, and then he drowns trying to save her a second time. That's why it's believable. The story doesn't waste time trying to convince us that the two characters "truly, deeply" love each other, it just throws them into an emotionally-charged situation and lets them react.