Real, real close. The "day" is a consecutive period of time. So if a morning session starts at 8am on Tuesday and a Filibuster starts during some time during the day, the "day" lasts as long as there is not an adjournment. If there is an adjournment, the "day" is over and the "2 times" rule resets. So while a Filibuster might last several calender days, it will likely never see a calender week as the ability to keep enough Senators awake/alive/talking is not inexhastible.
The speaker during a Filibuster cannot leave the floor while speaking or they surrender the floor at that point. During Thurmond's Filibuster, he had an aid bring a bucket to a cloak room so he could keep one foot in the chamber and relieve himself even as he talked. And he had to continue to talk. Thurmond didn't just stay awake and on his feet during his Filibuster, he also had to continue talking for the entire 24 hours, 18 minutes.
Then, whenever the number of Senators drops below 51, a quorum vote can be called and all Senators summoned to the chambers. Call a quorum vote every 45 minutes and you have 100 cranky, exhausted Senators on your hands after a 24 period. Drive it a day or two longer and you could have Senators collapsing in the chamber.
In other words, once a Filibuster starts, there will either be a vote at the end, and adjournment for the day, or a withdrawl of the proposal from the floor. The last two are unanimous actions and are "victories" for the Filibustering party. A vote is a defeat for the Filibustering party.