A judge on Tuesday delayed ruling on a wide-ranging gag order in the case of a Florida mom charged with killing her 3-year-old daughter.

A state attorney has requested that Circuit Judge Stan Strickland limit statements by prosecutors, defense attorneys, Orange County investigators and the family of defendant Casey Anthony in the case.

Anthony, 22, has pleaded not guilty to first-degree murder and other charges and faces life in prison if convicted of killing Caylee Anthony. The Orlando tot was last seen on June 16, but her mother did not report her missing until July. More than 1,000 searchers spent a weekend earlier this month looking for the toddler's body, but it has not been recovered.

Lawyers for both sides agreed that any gag order should be more narrowly tailored and the judge said he hoped to rule by Wednesday.

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Orange County Assistant State's attorney Jeff Ashton said at Tuesday's hearing that the girl's grandparents, Cindy and George Anthony, should be able to discuss their belief that Caylee is alive and their efforts to find her.

Defense attorney Jose Baez said the state has leaked much more information. But Ashton detailed several national television appearances Baez made that he said were designed to influence jurors.

Ashton said that to let it continue would "make it virtually impossible for us to find an impartial jury in the state of Florida, much less Orlando."

"There's a lot of hot air, but not a whole lot of law," Baez said of Ashton's presentation.

Baez said the First Amendment prohibits the government from ordering people what to say except in the case of "clear and present danger."

In his rebuttal, Ashton cited a Florida Supreme Court ruling that says a judge could impose the order for good cause, not just danger.

"If I go out in front of the cameras right now and say Caylee Anthony is dead, that would be grievous," Ashton said. "That's not my job."

An attorney for a local television station said a gag order now would be moot because there has been so much media coverage giving both guilty and not guilty views.

Strickland also quashed defense subpoenas for several television reporters.

Prosecution and defense attorneys' arguments sometimes grew heated, causing Strickland to admonish both benches.

"This is enough," Strickland said, exasperated. "Someone's facing life imprisonment. Let's act like we're supposed to."

Anthony told authorities she had left her daughter with a baby sitter in June and the two were gone when she returned from work. She says she spent the next month trying to find her daughter and didn't call authorities because she was scared. Investigators say they have poked several holes in her story.

Earlier Tuesday, Cindy Anthony implored investigators to look into a recent reported sighting of her granddaughter. She said that she doesn't know if a photo taken of a girl resembling Caylee is really her but wants it investigated.

Sheriff's officials were not immediately available for comment.

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The Associated Press contributed to this report.