Looks like the detente is over. This particular criticism, that Palin’s trying to advance herself professionally by being flirtatious, is an old favorite of Parker’s but it seems newly ironic after CNN’s flirty romcom-esque promo for her own show debuted last month. Even New York mag picked up on the vibe in its big tell-all about the cable news industry today:

Klein remained interested in Spitzer and arranged for the two to meet, and in the late spring Parker took the Acela to New York and showed up at Spitzer’s office. “It was one of the strangest dates ever,” Parker tells me. “We joked this is closest either of us will get to an arranged marriage.”

On a recent morning, Parker is sitting opposite Spitzer and their executive producer Liza McGuirk at a corner table inside the cavernous tenth-floor CNN cafeteria, with Columbus Circle filling the window.

“Well, you were approving me or checking me out,” Parker says teasingly.

Spitzer shifts uncomfortably. “I wouldn’t use those phrases.”

The pair have a surprising, adult chemistry, simultaneously flirty and professional. In our conversation, Parker plays the teasing office wife humbling Spitzer, who playfully takes the abuse.

Note to CNN: If jokes aimed at Client Number Nine about checking women out are a regular feature of this show, I will be tuning in. Elsewhere in “Parker/Spitzer” news today, we learn from Howard Kurtz that the two people they had on to discuss the tea party were hard-lefty Thomas “What’s the Matter with Kansas?” Frank and NYT reporter Kate “Who’s this obscure Hayek fellow, anyway?” Zernike. Good work. The fun begins tonight at 8 p.m.