I have heard the expression intestinal fortitude to mean courage or endurance to achieve something. Is there a connotation for stubbornness in this expression?
As people have mentioned in the comments, intestinal fortitude can be called a euphemism for guts. Guts is defined as "fortitude and stamina in coping with what alarms, repels, or discourages", or by Google as "personal courage and determination; toughness of character".
Both definitions have some mention of tenacity - "stamina" implies an ability to go on without giving up, and "determination" implies willingness not to give up. Similarly, "stubbornness" implies a refusal to give up. Thus I think there are similarities, although "intestinal fortitude" - or "guts" - seems to include the positive side of "stubborn", and not its possible negative connotations.
As a clarification, I am not saying that "guts" connotes "stubborn", nor vice versa, but that both those words strongly connote "tenacity", and in that way there is a link between them.
I would say the answer is simply "no".
Stubborn quite simply means someone who won't change their mind.
(Or indeed, something like say a piece of metal you have to machine could be "stubborn" - hard to change it's shape.)
This quality, stubborn, has nothing to do with "having guts" - like Tom Cruise or John Wayne. If you have guts, you can crawl through swamps, fight nazis, etc.
There's really no relation to "stubborn".
Particularly if the questioner is a non-English speaker, wondering what the phrase means, it's a shame to confuse the questioner.
Quite simply, "intestinal fortitude" is a humorous alternate way to say the slang term "guts". (Like, a street fighter, etc.) No real connection to stubborn.
There's more to it, I think... "guts"is a reference to the intestines, which run from the pyloris (at the end of the stomach) to the anus, and, "guts" also is a euphemism for "toughness" or "courage".
The phrase, "intestinal fortitude" takes this one step further, with implications of tenacity and toughness under fire - in dangerous situations, people can lose their nerve, turn tail and run, and in so doing, their fear can even cause them to lose control of their anal sphincter, with the expected result. Someone with "intestinal fortitude" has mastered their fear instinct AND their sphincter, and when the going gets tough, they have the self control to override their animal instinct to **** themselves and run away, and so can stand their ground and prevail.
Tasks that are difficult and unpleasant are sometimes said to be "stomach churning," that is making people want to throw up.
People that can performing "stomach churning" task without giving up, and without throwing up, are said to have intestinal fortitude.
I wouldn't characterize this as "stubbornness," but possibly as "perseverance."