The Gunners are still competing for silverware on three fronts but face a tough tie against Bayern Munich in the last 16 of the UEFA Champions League and have been drawn at home to Liverpool in the FA Cup fifth round.
They are top of the Premier League but have Manchester City and Chelsea in hot pursuit and tackle Liverpool, on Saturday, and then Manchester United in their next two games.
There was some surprise that Arsene Wenger did not bolster his attacking options in last month's transfer window, but Wilshere insists there are enough goals in the squad to challenge for major honours.
"People keep saying we need a new striker but Olivier Giroud has been great and Lukas Podolski can play there," Wilshere said in The Sun.
"Aaron Ramsey and Santi Cazorla have scored a few. Even I've got a couple! We know we can create chances and score goals.
"We have to work on our team shape in terms of winning the ball back and getting into better positions.
"The next two months are really important and if we come out of those unscathed, we will have a real chance.
"It would mean a lot to win something. Everything, to be honest.
"To win something for the first team would be amazing, not just for us but the fans.
"I grew up watching Thierry Henry winning everything, the 'Invincibles' and all that.
"This year, I feel we are right in there. We beat Spurs in the third round of the FA Cup and showed everyone we are focused in that competition.
"The Premier League and the Champions League - anything can happen. You saw that when Chelsea won it.
"This season we have a bigger squad. When one goes out another comes in. It has happened many times. Ox (Alex Oxlade-Chamberlain) has come back and is looking good.
"He is like a new signing, going into the last few months of the season. Podolski is getting fitter.
"A few players are out but we still have a good squad."
At the end of the season Wilshere also hopes to be involved with England at the World Cup, but he does not believe it is wise to look too far ahead.
The midfielder said: "The World Cup is something to look forward to, of course, but you cannot get ahead of yourself. For example, what has happened to Theo Walcott is terrible.
"But I know what can happen more than anyone, when you look at the terrible year I had a while back. I know you can take nothing for granted."