The New York Times has a great article about Rupert Murdoc and Hillary Clinton that gives some insight into both these characters. I have no idea how accurate the portrayal is, but it makes a fascinating read.
Mr. Murdoch has a history of backing and engaging political winners, most notably Prime Minister Tony Blair of Britain, the Labor Party leader, even though Mr. Murdoch all but invented Thatcher-mania back in the 1980's. Because he has no romanticism for lost causes, The Post apparently will not try to maim Mrs. Clinton in a Senate race with Ms. Pirro that is beginning to seem over before it has begun. They still whack Ms. Clinton occasionally, but it is more on general principle - they do it to stay in shape - and not with the same glee as in the past.
Over the long haul, the Murdoch-Clinton détente cannot last. In its phenomenal success, Fox News has used institutional enmity of the Clintons as one of its guiding principals. But in the meantime, the fight between Ms. Pirro and Mrs. Clinton will help ratings and circulation numbers, and the prospect of a Clinton presidential candidacy will agitate and engage the News Corporation's core audiences.
I'm not sure if this article is an editorial or a news report or what; the page linked to by Drudge doesn't make it clear, or even list an author.