As I said when AirTran raised its offer last month — it was going to be hard for Midwest Airlines to keep the bulk of its institutional owners from not taking the sweetened deal.

Today, AirTran announced that holders of nearly 57% of Midwest Airlines’ shares now back its hostile takeover bid.

AirTran said 13.9 million Midwest shares, or 56.6% of its equity, were tendered under AirTran’s cash and stock offer that expired Thursday. AirTran extended the offer, which is currently valued at about $15.89 a share, to June 8.

While AirTran seems happy with the shares already tendered, claiming that it represents a “no confidence” vote in Midwest management, Midwest says publicly it matters not. “It doesn’t change anything,” said Midwest spokeswoman Carol Skornicka. “The board continues to remain steadfast in its view that the offer is inadequate.”

I think Midwest is on the wrong side of the slippery slope in this one. Then again, they do still have a “poison pill” they can unleash.