Leann Rimes and Eddie Cibrian have been arguing

The couple — who broke up their respective marriages so they could be together — are said to be going through a rough patch after Eddie was fired from his role on CSI: Miami.

“LeAnn was counting on marrying Eddie ASAP because she’s dying to start a family,” a source told American tabloid the National Enquirer.

“But Eddie is cooling on the idea. He has taken a lot of heat for hooking up with LeAnn while they were still married, and he absolutely hates it.

“It hurts him to know that people are talking about them and judging them.

“He’s too upset about his career and everything else to even think about making a commitment to LeAnn right now.

“She has told him, ‘Don’t worry, I have plenty of money.’ But that just eats at him. He wants his own career and has an ex-wife and two kids to support.

“It didn’t help when he learned that LeAnn had to pay [ex-husband] Dean $7m in their divorce settlement. He’s been on the war path.”

LeAnn, the source says, is desperate to walk down the aisle and “wants him to at least set a date” for their wedding.

“She says she’s going to give Eddie until the end of the year!” blabbed the pal.