Connor Murphy from the Messenger newspaper has reported that The Robins must beat Aldershot at Moss Lane on Saturday and hope results elsewhere go their way if they are to survive in non-league football's top flight.
And manager Heathcote is hoping a bumper crowd will give his players just the lift they need.
Altrincham took more than 1,500 people to Stoke's Britannia Stadium for their promotion play-off final in 2005 and will be banking on a similar show of strength on Saturday.
Speaking exclusively to SAM, Heathcote said: "This is Stoke revisited.
"We need everybody to get behind the lads and make it a special atmosphere on Saturday.
"We still have a chance to stay in the Conference.
"I would be astonished if another team didn't have a hiccup but in order to make it count, we need to win.
"That's all we can do. We just need to do our job and win the game and then wait to see what happens elsewhere.
"The nature of football is so dramatic that it's likely something will happen, so we need to be ready to take advantage.
"I'm hoping the town shows the players they care.
"The support has been fantastic this season and we've been averaging more than 1,100 at home.
"But we need a crowd of at least 2,000 to give the lads a lift when they walk out onto the pitch.
"Football is about elation and deflation - hopefully we will experience the former after Saturday's game."
Alty have not had the best of weeks.
Following Saturday's 1-0 defeat at the hands of now relegated Tamworth, both Halifax and Grays Athletic won on Tuesday night to leave the Robins languishing in the Conference drop zone.
But no matter the result against Aldershot, Heathcote remains proud of his players achievements this season and is optimistic about the club's future.
"I'm optimistic because the reality is that this football club is still progressing," he said.
"I believe 100 per cent that this team is better than last year and play better football, even though we are fighting at the bottom of the table.
"These players have done a good job and they've got nine points more than they did last season.
"I know they will give their all in every game they play.
"When you consider we were fourth bottom of the Unibond four years ago and getting crowds of 350 but now we're fighting for survival in the Conference with crowds of 1,100 it tells you all you need to know.
"No matter what happens on Saturday, this club is still on the right track."