The 1995 Premier League champions have failed to win since the end of September and a run of six successive league defeats led to the sacking of Paul Ince.
Rovers chairman John Williams admits that the threat of relegation – and the financial hammer blow it would bring – is now staring the club full in the face.
But with neither Blackburn nor Allardyce, 54, seeking an escape clause in the manager's three-year contract should Rovers be relegated, Williams insists that Allardyce's appointment is a long-term one – regardless of the outcome of the club's survival battle.
Williams said: "There are lots of good arguments to say we should have gone for a man until the end of the season, but that's not the Blackburn way and we still prefer to try to build.
"Sam knows we're going to have to build up a head of steam to retain our status. I would rather be positive, despite our current situation, but if we do go down, then we go down together.
"There was a time when clubs got relegated and tomatoes were thrown at directors' cars and fans simply lost the bragging rights in the pub. But these days, you might end up losing your business if you're not careful and our turnover would fall from £56 million to £22 million if we get relegated.
"We now need two wins to get out of the bottom three and it's a daunting task, but that's what led us to Sam Allardyce. He's been there and done it and we think that, by appointing him, we've given ourselves the best possible chance."
Williams has come under fire for sacking Ince after just 17 Premier League games, but he countered: "I won't have it be said that Blackburn Rovers are trigger-happy, nor are we not prepared to give young British managers a chance. We've given two a chance – Mark Hughes and Paul Ince – and I'm happy to stand by that record.
"Nobody at Blackburn Rovers is saying Paul isn't going to be a good manager. It just wasn't going anywhere for him after an unusual start to the season. We had a good start, we were seventh after seven games, and then we hit the buffers with an almighty smack. We haven't won for nearly three months in the Premier League and the form was not getting any better.''
Blackburn then face Sunderland, Manchester City, Fulham, Newcastle, Bolton and Middlesbrough before the end of January.
Williams admitted: "If we go win, lose, draw for the rest of the season, we'll end up on 41 points. I don't know if that will be enough or not, so it is going to be difficult for us."