“Parker Spitzer” amounts to image rehabilitation for Mr. Spitzer, though it has not proved to be much of a platform yet. In its first seven weeks, “Parker Spitzer” averaged only 140,000 viewers ages 25 to 54, a drop of 2,000 from the seven weeks before it started, according to the Nielsen Company. “Countdown,” on at the same time on MSNBC, reaches twice as many people in that demographic, which cable news advertisers covet; “The O’Reilly Factor,” on Fox News, reaches five times as many.

But those two shows started in obscurity, with almost none of the scrutiny that “Parker Spitzer” has endured. Mr. Spitzer and Ms. Parker “launched into the most competitive time on TV, that’s just a fact,” said Bart Feder, a senior vice president at CNN. “That’s a heavy lift. They went into it knowing that. We went into it knowing that, which is why we take it one day at a time.”

In part, the show has been watched carefully because it represents Mr. Spitzer’s return to the public spotlight. But it is also because CNN is adrift, having shed a third of its audience in prime time the last five years.

Making matters even more delicate, Mr. Spitzer was paired with Ms. Parker over the summer by a CNN president, Jonathan Klein, who was dismissed weeks before the program’s Oct. 4 start date. The new executive in charge of CNN, Ken Jautz, is said to be supportive of the program. He declined an interview request.

Now, with Mr. Klein out of the picture, Mr. Spitzer and Ms. Parker, neither of whom had regularly hosted a show before, are learning how to do so in front of its viewers. Neither host was screen-tested before being hired, a fact that later raised eyebrows inside Time Warner, CNN’s parent company.