The League One club is trying to negotiate with eight senior players, but their refusal to compromise over wage demands has left Pompey at the brink of extinction.
Nwankwo Kanu has also lodged a claim for £3m in back pay and Birch says it is the players who have the future of the team in their hands.
"The club is heading for liquidation in just a few weeks, perhaps two weeks if these players don't leave or compromise on their wages," Birch said.
"We still have players like Ben Haim, Dave Kitson and Kanu on our books.
"Kanu has served the club notice that he wants to leave but before doing so he wants the money he says is owed to him by the club. These players hold the survival of the club in their hands.
"I must stress it is not their fault as the players didn't get the club into this trouble, but they do now have the ability to get the club out of this mess.
"The problem with everybody is that this club has cried wolf so often that no one believes it will happen, no one believes they will go out of business, but they will in two or three weeks. It is that serious now. The trouble is 'Portsmouth fatigue', but the truth is that the club is now fighting for its life."