Your description sounds like one of the stinkhorn fungi, Mutinus caninus. If not, try again with a different description and we'll see if we can't ID it for you.

Here is a link that might be useful: Dog thingie fungus

You are describing what I cooked for dinner the other night. I thought my husband had wolfed it down, now I know where he threw it!
And Rhizo, just exactly what is a dog thingie? Is this a technical term I never heard in my mushroom club? I call any object a 'thingie' when I forget its name, which happens more often these days.
Seriously, you had me busting a gut on this one....

Barbara

It could be mutinus elegans (Devil's Dipstick).The green slime is the spore mass which smells like rotting flesh . This is what attracts flies to it for spore dispersial.They are very common in wood chip mulch.The egg stage before they pop out of the ground is edible and pretty good.You want to be 100% sure you correctly ID it before eating it.This is the case for any wild mushroom.