A word for an inescapable and pointless situation?

I've heard this word used before but I can't remember it!

I've heard it used to describe wars like Iraq and Vietnam. Something you can't escape easily and is causing large problems, like a pit? Here is an example:

The American government has decided to pour extra money into the war in Iraq, unable to escape the ______ it has entered.

"Quagmire" is certainly a fitting word for your example:

"The American government has decided to pour extra money into the war in Iraq, unable to escape the quagmire it has entered."

Definition from M-WO:

2: a situation that is hard to deal with or get out of : a situation that is full of problems

The first definition (also from M-WO) is helpful in understanding how "quagmire" came to be used for other tricky, dangerous situations:

1: soft miry land that shakes or yields under the foot

EDIT: "Quagmire" was apparently quite commonly used to describe the US' involvement in the Vietnam War as is illustrated in the book, "The Making of a Quagmire: America and Vietnam During the Kennedy Era" by David Halberstam, Daniel J. Singal (Editor & Contributor)

The answer to the title is kafkaesque.

of, relating to, or suggestive of Franz Kafka or his writings; especially : having a nightmarishly complex, bizarre, or illogical quality <Kafkaesque bureaucratic delays>

But the answer in your example is quagmire.

In Greek mythology Sisyphus was punished with the task of rolling a boulder uphill for eternity. Each day the boulder would roll back down and he would have to roll it up again. This endless, pointless toil lends us

Sisyphean Endless or unavailing (Dictionary.com)

and thus giving you a sisyphean task