Jailing the Ministers responsible is one of the remedies open to Mr Justice Kelly, who yesterday said they would be found in contempt if they did not comply with his order.
Last night, legal sources were saying this was highly unlikely and some senior barristers thought the Ministers would comply with the order and find a suitable place for the girl in question.
But if they failed to do so, other remedies are available to the judge. These include imposing a fine for every day they remained in contempt, or sequestering their Departments' assets.
There is also a legal difficulty in jailing a government Minister for contempt arising out of his exercise of his office. A Minister is a "corporation" while carrying out his functions, and it is difficult to send a corporation to jail.
However, if the question arose it would have to be argued in court. It could be put forward that everyone has an obligation to uphold the Constitution, and Mr Justice Kelly's judgments are based on the Constitution.
Even without the situation deteriorating to this extent, it is an unprecedented constitutional collision between the executive and judicial arms of Government.
Article 6 of the Constitution spells out the different arms of government: legislative, executive and judicial, and says their authority derives from the people. Our system operates on the basis of "separation of powers" between these arms.
However, this is based on respect between the different arms and when a High Court judge orders a Minister to do something, he is entitled to expect his order will be upheld, unless it is successfully appealed.
While the courts have frequently judicially reviewed decisions of the executive, and often struck them down, this is the first time Ministers have been asked to answer personally for a failure to implement a court order.
Mr Justice Kelly has stressed that he is maintaining the separation of powers and seeking to get the various State bodies to apply the law as it stands. He is not seeking to change it.
"This is just a sign that Judge Kelly is getting fed up," said one senior counsel. "You can't blame him. He saw a girl who was in before him ending up dead."
"He has shown amazing forbearance for years about these cases," said one senior counsel. "Then he turns around five years later and finds the State did nothing and he finds these kids are dying on him."