There is absolutely no indication that there was a passage of days anywhere in the movie. The closest we get is this:
Star Trek: First Contact wrote:
PICARD: One, and it's on a direct course for Earth. It'll cross the Federation border in less than an hour. Admiral Hayes is mobilizing a fleet in the Typhon sector.
DATA: At maximum warp it will take us three hours twenty-five minutes.
Just because that is where they are meeting up doesn't mean that is where the battle with the Borg takes place. There's no indication that a group of starships could hold off the Borg for days. Plus, it makes no sense that the Enterprise would be at red alert for that long.
Just like the Abrams films, they compressed the time frame to keep everything up-tempo.