Last week's abject 3-0 home defeat to Newcastle was the club's third in succession and left them rooted in the bottom three ahead of Saturday's daunting trip to Manchester City.
But, after a week which saw the respective arrivals of Lokomotiv Moscow striker Dame N'Doye and new assistant boss Mike Phelan, Bruce is confident he has got the backing required to help him beat the drop.
Bruce said: "The one thing I'll never do is take anything for granted and, with the expectation we have built up at this club, we are now in the bottom three and that is a problem.
"But I think if I was in trouble the chairman would tell me. He has backed me with a new assistant manager and a forward so if he was going to get rid of me I think he'd have done it before I brought them in.
"I can't worry about it. If it happens it's not my decision, but one thing's for sure - we've worked extremely hard for the last couple of years and I am not going to give it up without a fight."