Hyde's midweek defeat at Lancaster left them with just two points from their last 16 games and leaves them needing to produce virtual championship form for the rest of the season to preserve their UniBond premier division status.
But, while admitting Saturday's home clash with lowly Harrogate is a "must win" game, Hill is refusing to throw in the towel.
The former Manchester United and England star said: "I've been in football long enough to know how quickly your fortunes can change in this game.
"We might be down at the moment, but I still maintain we only need one win to turn the corner.
It's not going to be easy, but, believe me, we'll get through this."
Hyde's plight isn't helped by the fact they face a mounting catalogue of injuries.
Goalkeeper Peter Crookes is the latest to be struck down, having suffered a thigh strain which makes him a doubtful starter tomorrow.
There's Tameside derby action at Hurst Cross, where Ashton United will be facing Droylsden for the third time this season, with honours even so far.
Bloods boss Dave Pace appears to be losing his bid to have Yeovil striker Carl Alford signed in time to play but is poised to give a debut to his newly acquired ex-Bury centre-half Paul Challinor.
Elsewhere, Stalybridge, now up to third, face seventh-placed Whitby.
Manager Dave Miller has a surfeit of selection options as Marcus Hallows, who has been out for two months, Jerome Fitzgerald and Nathan Wharton are all newly recovered from injury.
Leigh's leading scorer Dino Maamria is suspended for their Nationwide Conference basement battle at Forest Green, so boss Steve Waywell says he's likely to operate Neil Tolson as a lone striker.
Radcliffe will be chasing a seventh successive UniBond first division win when they host fellow promotion hopefuls Spennymoor.
Bottom-placed Trafford, who have lost their last 11 games, receive Rossendale.
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