The government separated the families as part of the Trump administration's effort to criminally prosecute all immigrants who cross the U.S. -Mexico border illegally, including those who are seeking asylum.
HHS admitted it had resorted to DNA testing on some of the children to try to match them with their parents.
"If we find out they are not the legal parent, then clearly we are not going to reunite them", Meekins said.
"Let me be clear: HHS could have transferred every child out of our care to a parent who is now in DHS custody today if we did not take into account child safety or whether the adult is actually the parent", HHS Chief of Staff Chris Meekins, told reporters.
"It's extremely disappointing that the Trump administration looks like it will fail to reunite even half the children under 5 with their parent", ACLU attorney Lee Gelernt said in a statement.
The ACLU said late Sunday the administration provided it with a list of 102 children under 5 years old and that "appears likely that less than half will be reunited" by Tuesday's deadline. Attorneys for the children and the Department of Justice are working with the court to reunite the remaining children - many of their parents have been deported or released from custody in the United States - as quickly as possible.
As the family separation process got underway, the obstacles that the government was setting up for itself became evident.
The filing noted 13 others now deemed ineligible for reunification, for reasons ranging from parents now in the custody of other criminal justice agencies to a parent who is being treated for a communicable disease, and one who lives in a home with another adult who has a criminal background.
Sabraw said Tuesday that "full background checks of other adults in the household are not necessary under these unique circumstances".
In court filings, the ACLU has said the government is asking for needless provisions for reuniting families that would not happen if the families had not been separated in the first place.
The reunions are expected to be carried out in secret or secure locations, with parents taken from the detention centers where they have been held and children brought from federal shelters or foster homes.
In a seven-page order, the judge called that request "a cynical attempt, on an ex parte basis, to shift responsibility to the judiciary for over 20 years of congressional inaction and ill-considered executive action that have led to the current stalemate".
The separations sparked national and worldwide outrage that crossed party lines and including warnings from health experts that taking children from their parents would incur significant emotional harm. Several other children can't be reunited with their parents because the adults have serious criminal records, the government said. Some detained parents had been released from custody and could not be contacted.
Still, at a court hearing on Monday, the federal judge who set the deadline for reunifications said he was "very encouraged" thus far.
Federal officials said they are reunifying as many children as they can and attributed delays to "legitimate logistical impediments" that make it "impossible or excusable" to meet the court's deadlines.
Nine have parents who were released already from ICE custody and are somewhere in the US.