Is there an idiom or phrase associated with a person who can't do some work or something but he or she blames something or somebody else?
A bad workman blames his tools, might fit the bill:
something that you say when someone blames the objects they are using for their own mistakes.
- 'This oven burns everything.' 'You know what they say, a bad workman blames his tools.'
(Cambridge Idioms Dictionary)
In a word, such a person is irresponsible. In a phrase, such a person "has no sense of responsibility."
Irresponsible means not responsible.
Responsible is defined by Merriam Webster as:
"2a able to answer for one's conduct and obligations: trustworthy
2b able to choose for oneself between right and wrong"
Webster's New Collegiate Dictionary defines responsibility as: "....Accountability, also moral accountability, as the responsibilities of parenthood; Reliability...."
You might say "If you want the job done, and done right and on time, do not ask X; he is completely irresponsible." Or ".... do not ask X; he has no sense of responsibility."
In looking up definitions for the phrase, I find "awareness of obligations" (e.g., The Free Dictionary). However, as I have always used it, the phrase goes further: the person is not only aware, but cares.
Thus, I like the example quoted in Philiosiblog: "The most important thing is to have a sense of responsibility, commitment, and concern for each of our fellow human beings." Dalai Lama
A "scapegoat" is someone whom someone, or multiple people, wrongly blame for something going wrong. You can use it as a verb too.
(It originates for a primitive ritual in which everyone symbolically piles their sins and problems on a real goat, who was sacrificed to cleanse the community of evil)
To find fault with someone or something. https://idioms.thefreedictionary.com/find+fault