The phrase is "the marriage is on the rocks" (plural). The image is of a shipwreck. The marriage is the ship, and it has been driven aground on a rocky shore and is breaking up. I'm not sure, but I think this expression may have been popularized by the once-hugely-popular newspaper columnist, Walter Winchell. He definitely is responsible for "phffft" (meaning the imminent breakup of a couple). The phrase "the two of them are an item" is also a reference to Winchell, meaning that Winchell would mention the budding romance between a couple as an "item" in his column. The same phrase "on the rocks" also means an alcoholic drink served over ice. "Scotch on the rocks" means Scotch whiskey poured over ice instead of being served "neat" in a "shot glass."

A "marriage on the rocks" is a marriage that is experiencing difficulty. In other words, the marriage is crumbling and potentially falling apart.

I believe the correct saying is "marriage on the rocks". The idiom means that the marriage is struggling or the couple is on the verge of breaking up.