Though the reality star, 31 and Odom, 35, both signed divorce papers in July, they are still legally married since a judgment has not yet been entered in court.
Kardashian – who has not left the former basketball player's side since he was hospitalized after being found unconscious at a Nevada brothel – is in charge of Odom's medical care and a source close to the family tells PEOPLE she is "not doing well at all with the responsibilities of making medical decisions."
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The source adds the Kardashian has been seeking advice as to what to do from others and is "really having a hard time making decisions."
"She realizes that these are literally decisions of life and death, and she wasn't prepared to take on this responsibility," continues the source.
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Though Kardashian "has spoken with every member of the family, some a few times, as well as legal, spiritual and medical counsel" and "everyone is really supportive," the decisions are "hers alone to make."
"Kris [Jenner] is giving some advice, but everyone else is basically just being there for her, letting her vent and talk about it," the source says. "But no one is going to tell her what she should do, because that's her decision."
Odom, who had cocaine and opiates in his system, remains in a coma.
According to the source, Kardashian is "facing some guilt issues with this."
"She wonders if there was anything more she should have done," continues the source. "Kim [Kardashian West] has told her that this isn't her fault."
While thoughts and prayers are with Odom, the source adds that everyone is also worried about Kardashian.
"We're all praying that she finds the strength and wisdom she needs right now," the source says. "Obviously, though, Lamar's the one who needs the most prayers."
As of Thursday, Kardashian and her mother Kris, as well as sisters Kim, Kourtney Kardashian and Kendall Jenner currently remain in Las Vegas in support of Odom.
As of Thursday, Kardashian had arranged for Odom's father, ex-girlfriend and two children to fly out from New York to be by his side as he fights for his life.
Kardashian herself is surrounded by sisters Kim, Kourtney Kardashian and Kendall Jenner, as well as mother Kris, who appealed to her followers on Twitter to "Please pray for Lamar #ourfighter."