A leaked draft of the proposal first reported by Reuters and then published by Vox showed that immigrants seeking an adjustment of status, such as those applying for permanent residency, “must establish that they are not likely at any time to become a public charge” or rely heavily on long-term government assistance, lest they be deemed “inadmissible.”

The proposed regulation could be sent to the Office of Management and Budget for processing this month, according to Charles Wheeler, a legal expert at the Catholic Legal Immigration Network. The Department of Homeland Security did not respond to inquiries regarding the proposal’s timeline and prospects.

A study conducted by the National Academies of Sciences showed that 45.3 percent of all immigrant-headed households with children use a food assistance program. The vast majority of those children are American citizens.

Administration officials say that fiscal responsibility motivated the policy move.

“The administration is committed to enforcing existing immigration law, which is clearly intended to protect the American taxpayer,” said Tyler Q. Houlton, the acting press secretary for the Department of Homeland Security. “Any potential changes to the rule would be in keeping with the letter and spirit of the law — as well as the reasonable expectations of the American people for the government to be good stewards of taxpayer funds.”

In an email to local WIC agency directors, the Rev. Douglas Greenaway, the president of the National WIC Association, assured providers that the proposed rules did not yet have “the weight of law.” But he acknowledged that this caveat “may not resonate with immigrant families” who are now weighing their need for WIC services against their desire for a permanent future in the United States.