The manager has endured a difficult first season at Stamford Bridge since succeeding Carlo Ancelotti last summer and last weekend's defeat at Everton sparked reports he had lost the dressing room.
Club owner Roman Abramovich has become a regular visitor at the Blues' Cobham training ground, fuelling speculation the Russian billionaire is once again growing impatient in his quest for more success.
Defeat to Championship outfit Birmingham would do nothing to strengthen Villas-Boas' position and could only undermine confidence ahead of next week's Champions League last 16 first-leg meeting with Napoli.
But the coach, who has already accepted Chelsea are bystanders in this season's Premier League title race, insists he retains the full support of Abramovich even if not all the players share his vision of change for the club.
"They don't have to back my project. It's the owner who backs my project," he said. "I think the owner has full trust in me and will continue to progress with the ideas that we have.
"In the end, that is the objective of getting us the best position possible in the league, plus these two trophies which we are fighting for.
"It will be extremely good for us if we win against Birmingham to put ourselves in the quarter-finals of the FA Cup.
"But we need strong progression in the league and to show our strength. Third place is already 10 points ahead of us. We have to get Champions League qualification."
Didier Drogba is back at the club from the Africa Cup of Nations but will not be considered for selection, although Villas-Boas hopes the striker's presence will help motivate Fernando Torres and Romelu Lukaku.
"Drogba gives us another solution up front. We've used Torres in all the games since he went away," Villas-Boas said.
"For the Birmingham game it will be between Torres and Lukaku and from then on with Drogba as well. For the type of player he is, he's as strong as anybody."
John Terry and Ashley Cole will again be missing with injuries but midfielder Ramires should return.
Chelsea's cause will be helped by the fact that Birmingham are focused more on securing promotion back into the Premier League than the cup.
Manager Chris Hughton, however, insists his side's experience in handling the demands of competing in the Europa League this season demonstrates his squad can cope when changes are made to the line-up.
"We are in the same situation here as when we had to marry up the league fixtures with the Europa League," he said.
"But this is what we have and, one thing I can guarantee you, is that there will be genuine excitement in that Chelsea dressing room to go out and get a win.
"Even with the fixture problems it could cause us, there isn't anyone in the club -- players and fans -- that won't want us to try and win a game on Saturday against one of the top clubs.
"If we are able to do that, we will be delighted. This will be a massive test but whichever way it goes, it is certainly one we will enjoy."
Source: AFP
Source: AFP