The Blues go into 2013 four points behind champions City and a further seven adrift of leaders United with a game in hand after a rollercoaster start to the season.
Chelsea threw away a four-point lead at the end of October in an alarming slump that cost Roberto Di Matteo his job as manager.
But they are arguably in their best form of the campaign under interim boss Rafael Benitez, winning seven of their last eight games in all competitions and raising hopes of a dramatic fightback in the title stakes.
Defender Cahill said: "We need to keep looking forward and have that challenge in the back of our head.
"We would rather have the points in the bag, but that's another challenge we have got to face. There are plenty of games coming up."
He added: "I think we have good momentum.
"We have changed the team around slightly, the lads are playing well.
"We just need to keep winning games. That's the way we look at it."
Chelsea appear to be back to their bloody-minded best with Benitez in charge, with Cahill embodying that resilience.
He was still sporting a black eye on Sunday picked up in the Boxing Day win at Norwich and he said: "We are not just all about flair and things like that - we can dig in.
"Defensively, we have looked really solid in recent weeks."
Indeed, it appears they have finally learnt how to cope without John Terry, while they played the whole of the second half of Sunday win at Everton without injured goalkeeper Petr Cech.
They would not have won at all but for Terry and Cech's fellow veteran Frank Lampard, whose two goals gave Chelsea further food for thought on their decision not to offer him a new contract.
Cahill said: "You don't come across many players like Frank, somebody who scores 20 plus goals a season - consistently - over many years."
He added: "Ultimately, he has got us the three points. He was in the right place at the right time - he always seems to be."
Wednesday's west London derby with QPR could see Chelsea make it 12 points from 12 over the festive period.
They also thrashed Aston Villa 8-0 in their last Stamford Bridge outing.
Cahill added: "There is a different atmosphere in derby matches. A lot of form goes out the window in them.
"But we are at home and I don't think many teams like to come to Stamford Bridge.
"Hopefully, we will make it very difficult for them to play on our patch."