Rangers became the first club in Premier League history to fail to win any of their first 16 games when they were held to a 2-2 draw by Wigan on Saturday.
That left them eight points adrift of safety - one point more than they have accumulated over the first four months of the season - and no team with so few points at this stage has ever stayed up before.
Defender Hill said: "You can look at it two ways. You can either look at it and go, 'Oh my God, how the hell are we getting out of this'? Or you go, 'Sod this, let's prove people wrong'.
"And if you do manage to do it, what a record it would be and what an achievement when you're sitting in your armchair in 10 or 15 years.
"It's a challenge but you've got to deal with it. If you're not up for it, don't come in, it's as simple as that. I think we've shown over the last few games that we have got that passion, we just need that bit of luck.
"We've got a lovely 16-game winless streak, which is fantastic isn't it?! I still can't believe it. The facts are there.
"We've just got to stand up, puff our chests out and go out there and try to get three points."
Rangers are at least unbeaten since Harry Redknapp replaced Mark Hughes as manager last month, drawing all three games.
The 65-year-old has plenty of experience of such situations having taken over at Southampton, Portsmouth and Tottenham when all three were struggling, keeping the latter two up.
Hill said of Redknapp's impact: "Everyone talks about his man-management style and all that kind of stuff but he's just come and tried to give us a bit of confidence and a bit more belief in our ability, to go and try to impose ourselves on games and try to get results.
"The table doesn't lie, we've been poor, simple as that but we've got some good players. We've just got to have that confidence to go out and try to win games. Hopefully there's glimpses of that and we can do that against Fulham next weekend."
Following Saturday's game, Redknapp said he will only ask the owners to dip into the January transfer market if he feels they have a chance of getting out of trouble.
Rangers were big spenders in the summer in a bid to avoid their struggles of last season, when they stayed up on the last day, and Hill thinks consistency could be what they need.
He said: "I've been here three years now and I've seen a hell of a lot of players come and go. Is it the answer? I don't know. I just think we need a bit of stability at the moment.
"You need a settled team, which we've tried to do over the last three games, and a system of play that suits us. I think we're definitely getting there, it's just disappointing we couldn't get the first three points.
"The chairman's throwing money everywhere but sometimes that doesn't work. You've got to stick with people and work with them and try to get the best out of what you've got."