Last month’s 4-1 defeat in Wales, coupled with a 5-1 drubbing the last time his side met Denmark in the second leg of their World Cup play-off, have left O’Neill and assistant Roy Keane under pressure.
There has been speculation that a failure to improve on that in the next two games could prove fatal for the management duo, but O’Neill remains bullish.
He said: “If you look at it, we’ve qualified for the Euros – a couple of years ago, I must admit. I think it was the best we ever did in the Euros.
“Then we were fourth seeds (for the World Cup qualifiers) – we got to the play-offs and we’d lost one in 11 before that, so these two games apart, I don’t really fear.
“There’s always pressure. There’s pressure on managers every single day of the week.”
O’Neill has had opportunities to return to club management since he took up the Ireland reins with Stoke coming as close as anyone to prising him out of the Football Association of Ireland’s grasp.
But as he prepares to celebrate his fifth anniversary in the job, he is content with his decision to stay on.
He said: “I had a possibility of leaving to go to another job and I thought I’d like to stay on and see if we can qualify for this competition. The Euros start in earnest in March-time or so. We’ll see.
“We got beaten by Wales. Wales then got beaten by Denmark. It’s up to us on the night to try to win and put us back to level pegging again.
“But of course, we’ve got to try to make some sort of progress. It’s important not to worry about what might happen a couple of games after. Let’s just deal with this game and try to win it if we can.”
All but one member of the 26-man squad trained on Tuesday morning at the Aviva Stadium, James McClean doing so in a protective cast on his left arm after suffering fracture on international duty last month.
Southampton striker Shane Long sat out with an ankle injury picked up in Sunday’s Premier League defeat by Chelsea, but he is expected to be fit for the weekend.