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(CNN) —  

The Trump administration is considering deporting migrant families with court-ordered removals, a move that senior Department of Homeland Security officials have resisted in the past, multiple officials tell CNN.

The idea, described as a way to “send a message” to smugglers, is “under serious consideration,” according to a senior administration official. Another source said there are ongoing discussions within the department. A separate source tells CNN no immediate action is being taken.

The Department of Homeland Security, suffering from a lack of resources, is unable to deport all those who are ordered to be removed from the country and has said it focuses on the people it deems the most dangerous.

However, that could change as a massive influx of migrant families make their way into the country illegally over the southern border.

As part of the consideration, the administration has been looking at an operation rolled out in the late years of Barack Obama’s presidency – and revived in President Donald Trump’s first year in office – that also targeted family units. Obama initially focused on felons.

White House senior adviser Stephen Miller has been a proponent of the new initiative, according to three US officials. The senior administration official said Miller wasn’t alone in pushing for it.

Former Homeland Security Secretary Kirstjen Nielsen had rejected the plan because the policy of the department was to prioritize criminals for deportation, said one of the officials. DHS, stung by the fallout over family separations, has been wary of public backlash for targeting families, according to the official.

But Miller has been pushing anew for the family deportations under acting Homeland Security Secretary Kevin McAleenan, the official added.

McAleenan has also been resisting it, one of the sources said. Part of the concern is that it could hurt negotiations with Democrats for Immigration and Customs Enforcement funding, which has been strapped for resources, as well as the political optics, according to the source.

The source said those resisting know that the storyline will be family separations once again. But the administration has been discussing and grappling with how to handle families who are defying court orders for removal or aren’t showing up on their court dates.

The source said the administration has been looking at Obama-era policies such as Operation Border Guardian/Border Resolve, which targeted family units for removal amid an uptick in families and unaccompanied minors attempting to cross the border. DHS revived the operation early in the Trump administration.

There are no current plans to implement the targeting of families, the source added. The White House referred requests for comment to DHS. DHS declined to comment.

In April, nearly 100,000 migrants, many of whom were families, were apprehended at the southern border, according to Customs and Border Protection data.

There are ongoing discussions about the removal of families with orders at the agency level, according to a DHS official.

The families expected to be targeted are those who recently entered the United States and were placed in an expedited family docket, the official said.

Last year, the Executive Office for Immigration Review, which oversees the nation’s immigration courts, announced that it had begun tracking family cases filed by DHS in 10 immigration court locations: Atlanta, Baltimore, Chicago, Denver, Houston, Los Angeles, Miami, New Orleans, New York City and San Francisco.

The cases are being expedited to try to process the families in under a year.

From September 24, 2018, through April 26, 2019, more than 40,000 cases were marked as so-called “family-unit” cases, a DHS designation, according to Executive Office for Immigration Review data. Roughly 8,000 cases have been marked completed. Of those, 7,724 cases ended with removal orders, 6,764 of which were ordered removed because they did not attend their immigration hearings.