To be up the creek means to be in a prickly predicament with no means of alleviating the problem. Up the creek is actually only half of the idiom. The full idiom is up the creek without a paddle, though it is often shortened to simply up the creek. Another iteration of the phrase involves a slang scatological word. The origin of the phrase up the creek without a paddle is murky. The first examples of the term up the creek are found in the 1860s in America, especially with the addition of the slang scatological word.
Up a creek is a variation of up the creek, which surely began as a mishearing of the term up the creek without a paddle.
$1.2m fine threat leaves regeneration project up the creek (The Australian)
Finally, if a car dealer approaches you with a better deal, make sure you look at it from every angle before signing on the dotted line, and only accept if it won’t make such a vast difference to the guaranteed final value that it’ll leave you up the creek without a paddle when it comes time to part exchange. (The Telegraph)
“Without the $25 million we’d be up the creek without a paddle,” said McKoy. (The Paterson Times)
Somebody better get the power back on soon, or you and your family are going to be up the creek. (The Bristol Herald Courier)
His first “dream team” recruit: F. Lee Bailey (Nathan Lane), who arrives with legal advice and a suitcase full of crackling one-liners: “You’re sure up the creek in high-grade manure.” (Variety)
When I was diagnosed in 2013, I had just signed a contract with the Opera House for Dirty Dancin in Le Shebeen and I felt as though I was up the creek without a paddle. (The Belfast Telegraph)
Houseboats in Sydney up a creek without a paddle (The Straits Times)