Victory at Leyton Orient today would lift the Owls back into second spot and nudge the Blades, who are without a fixture this weekend, down into the League One play-off zone.
Jones said: “We have thrown down the gauntlet since the day I walked into the club. We want maximum points and – if we get that – it will be up to Sheffield United to get maximum points on Wednesday.”
The Blades’ scheduled fixture has been switched to Wednesday night because opponents Chesterfield are involved in the Johnstone’s Paint Trophy final tomorrow against Swindon Town at Wembley.
There are just two points between the Sheffield clubs, while Yorkshire neighbours Huddersfield Town are just three points behind in fourth spot with a game in hand.
“It’s an opportunity to put a bit of pressure on them (United),” admitted Jones.
“But, equally, we don’t want to put too much pressure on ourselves. We have to concentrate on what we have to do.
“The players have worked really hard to get to where they are and they know it’s going to take the same amount of work to get that little step further.
“We have eight games to play – which doesn’t sound a lot – but there is still a lot of football to be played. It is going to get nervy and twitchy but we just have to stick together.”
Although opponents Orient are five points clear of the relegation zone and within touching distance of safety, Jones stressed they will be no pushovers.
“It doesn’t matter whether you are safe or not safe,” he said.
“Players are paid to play to the best of their ability and, if any of my players took their foot off the gas, I wouldn’t be very happy. So we expect nothing less than a tough game and I will be re-iterating that to my players.”
Jones made his first moves into the transfer market on Thursday afternoon when Burnley winger Keith Treacy and Newcastle United striker Nile Ranger joined the Owls on loan. Both are available for today’s game.
“At one stage, I didn’t think anything was going to happen,” he admitted. “We waited and worried but to get both of them before the deadline was really good.”
The Owls have defensive problems with centre-backs Danny Batth, Rob Jones and Reda Johnson carrying knocks.