The Steelmen go into the game with the third-placed Yeltz still sitting in top spot in the BetVictor Southern League Division One Central.
But Corby’s title hopes suffered a setback last weekend as they were beaten 2-1 at Barton Rovers while second-placed Berkhamsted and Halesowen both won.
It has left the Steelmen just two points clear of Berkhamsted and six ahead of Halesowen who, crucially, still have four games in hand.
Taking all that into account, joint-manager Mulligan believes Corby really need to complete a league double over the Yeltz tomorrow (Saturday) having won 2-1 in the West Midlands earlier in the season.
“After the defeat at Barton, we are probably going to have to win the game,” he said.
“A draw would keep us in there but we certainly can’t afford to lose.
“There are still 16 games to go but we know we can’t afford a defeat tomorrow. It’s a massive game.
“Nothing is given out in January but if we can get the three points then it will help towards the cause at the end of the season.
“They have got some very good players in their squad and I think one of their strikers has 27 goals in all competitions this season already.
“They have got some dangerous players but we have done it already, we went away from home and beat them and the lads are confident we can do it again.
“We will be having a good week or training and we will need an energetic performance on the pitch.”
With this weekend’s game bringing together the two best supported teams in the division, a big crowd is expected at Steel Park.
And Mulligan wants the Steelmen faithful right behind his team.
“It’s our biggest game of the season so far so hopefully it will be a good crowd,” the joint-boss added.
“I am sure Halesowen will bring a good following with them so we want our supporters to get right behind the lads and hopefully we can go out and put in a good performance and get the three points."