The Whites have just three games of the Premier League season remaining in which they must prove themselves worthy of the top-flight status, only recently earned after sixteen years of fighting to return.
Level on points with Burnley, the relegation battle has become a straight shootout, with Leeds' significantly poorer goal difference demanding that the West Yorkshire side must not only match but outplay their Lancashire counterparts, with Everton not yet out of sight but finding form at the crucial moment of the season.
The fight begins on Wednesday evening, when United host third-placed Chelsea at Elland Road for the first of a trio of matches that will decide the Whites' destiny.
Harrison said that the unity of the team is a priority as they battle through a tough moment.
"We have an important game coming up on Wednesday, and we just have to stay strong and be ready for that," Harrison said.
"At this point, it's a difficult moment for us as a club, but we have to stay together, we have to have belief and keep going forward positively."
The Blues clash comes just three days after Leeds suffered a disappointing 2-1 defeat to Arsenal at the Emirates, where an early mistake by United 'keeper Illan Meslier put the visitors on the backfoot before a rash challenge by Luke Ayling, deemed a dismissible offence by referee Chris Kavanagh, weakened their chances of recovering a desperately-needed result.
Leeds' second-half fightback, though it couldn't earn them points, was evidence of a familiarity with adversity that Harrison says has characterised the 2021/2022 season.
"It's difficult - we have a lot of things to think about, and we have a lot of good things to take from the [Arsenal] game as well," Harrison said in his post-match interview.
"I think it's been like that for the majority of the season really, with a lot of injuries and difficult moments throughout the season.
"But, the club that we are, we always try and fight through these moments."
One player who successfully shifted the balance of play in the Gunners' defeat after the interval was 19-year-old substitute Lewis Bate, who could face up against his former side Chelsea on Wednesday evening.
Harrison believes that the young players who have been called upon to fill in for the Whites' various injured senior players this season will play a big part in the fight for survival.
"We're ambitious and the young guys are coming on, Lewis came in again, and I thought he played well again today and it's times like that where the young lads step up and they have all season," Harrison said.
"It's about staying together, the young lads stepping up and we just have to stay positive."