The story at the end of week two of News Corp’s bid for Dow Jones is clearly the loss of confidence that this will end in an acquisition. No other bidders have emerged. News Corp hasn’t made any gestures that it might increase it’s bid. Quite the opposite—word is spreading that News Corp won’t increase it’s bid and that News Corp CEO Rupert Murdoch has told a close associate that he is not certain he will prevail.

Murdoch seems to be trying to use charm rather than money to win over the Bancroft family, which controls the company through its super-voting shares and has announced—through a representative on the Dow Jones board—that it isn’t going to take News Corp’s offer. He’s telling jokes. Keeping it light. On the News Corp earnings call he spoke of his admiration for the Bancroft family and Dow Jones management. And he’s more or less apologized for the fact that his offer became public, claiming he hoped to negotiate the deal in private—contrary to rumors that the leak came from News Corp. The point of this is to make nice with the Bancrofts, to take away the impression that Murdoch went public with his offer in an attempt to get the public shareholders to pressure the family into selling the company. No one likes to be strong-armed.

(After the jump: A completely paranoid deal judo conspiracy theory.)

These remarks—his private doubts and his charm offensive—seem to have convinced a lot of analysts and investors that News Corp isn’t planning on, well, “sweetening” his bid for the company. Shares of Dow Jones drop a bit every time Murdoch uses words rather than dollar signs. Dan Dorfman, writing in the New York Sun, quotes a hedge fund manager who is shorting Dow Jones stock after concluding that the News Corp bid is a “non-deal.”

But we’ve also heard whispers of a conspiracy theory among some observers who suspect that Murdoch may be trying to scare the Bancrofts—and other shareholders—into believing that his first offer was his best offer. He may, in fact, sense weakness among the Bancroft family and be looking to tell them that this is as good as it’s ever going to get, some say.

The general impression within the Wall Street Journal, which is owned by Dow Jones, is that the deal looks far less likely to happen at the end of this week than last week. “There’s a lot less sense that this is inevitable,” someone familiar with the atmosphere inside the paper told us.

Next week: Intense media scrutiny of the Bancrofts (most likely) raises the question: will they sell to regain their privacy?

Murdoch regrets publicity over Dow Jones bid [CNNMoney]
Murdoch hints at no boost to Dow Jones bid [Financial Times]
Falling Dow: Doubts Grow About Murdoch’s Bid [DealBook]