The 27-year-old will carry the burden of firing the Black Cats to Premier League safety after it was revealed that leading scorer Steven Fletcher will miss the final eight games of the campaign with ankle ligament damage.
Graham, a £5million transfer window acquisition from Swansea, has started the last four of his six games to date for his new club alongside the Scotland international, but is yet to add to the seven goals this term with which he arrived.
However, Johnson is convinced he is ready to make his mark at the Stadium of Light.
He told Sky Sports News: "Fletch has proved himself this season. Without his goals, we would be in a lot worse position. He's going to be a big miss for us.
"I think it's important for the whole team to step up now and put the performances in we know we are capable of.
"It's important someone gets the goals with Fletch missing because we haven't scored that many or created many chances. When we get them, it's important to put them away.
"I think Danny is a couple of games away from getting a good run."
Misfortune struck for Fletcher on international duty when he was carried off the field on a stretcher just minutes into Scotland's 2-1 World Cup qualifier defeat by Wales on Friday.
But if his premature departure was a blow to international boss Gordon Strachan, it was a bigger setback for club counterpart Martin O'Neill, with his side battling to avoid being dragged into the fight for Premier League survival.
Fletcher's 11 goals for the club he joined for £12million from Wolves during the summer have proved invaluable, and his absence robs O'Neill of his most potent weapon just when he needs him most, with leaders Manchester United due on Wearside on Saturday and clashes with Chelsea and Everton to come either side of a derby trip to Newcastle.
Johnson said: "It's been so frustrating because we have got some really good players. We haven't had the results and have struggled massively at times.
"All the lads are really frustrated, but we have got to keep working hard and hopefully it will come."
The extent of 26-year-old Fletcher's injury was not the only bad news for Sunderland after it emerged that skipper Lee Cattermole has had to admit defeat in his bid to avoid knee surgery.
Cattermole had an operation on Wednesday and the 25-year-old too will miss the remainder of what has been a frustrating campaign for him.
A club statement said: "Cattermole underwent an operation on his knee earlier today and Fletcher sustained ankle ligament damage whilst on international duty with Scotland.
"It is not known at this stage if Fletcher will require an operation, with the injury requiring further assessment in the coming weeks.
"Both players will play no further part in the Black Cats' 2012-13 Barclays Premier League season."