Washington (CNN) White House adviser Stephen Miller is pushing to expedite a policy that could penalize legal immigrants whose families receive public benefits and make it more difficult to get citizenship, three sources familiar with the matter tell CNN.

The White House has been reviewing the proposal since March at the Office of Management and Budget, which is the last stop for regulations before they are final. But concerns over potential lawsuits have delayed the final rule, and the draft has undergone numerous revisions, multiple sources say.

The crux of the proposal would penalize legal immigrants if they or their family members have used government benefits -- defined widely in previous drafts of the policy.

The law has long allowed authorities to reject immigrants if they are likely to become a "public charge" -- or dependent on government. But the draft rule in its recent forms would include programs as expansive as health care subsidies under the Affordable Care Act, as well as some forms of Medicaid, the Children's Health Insurance Program, food stamps and the Earned Income Tax Credit.

The rule would not explicitly prohibit immigrants or their families from accepting benefits. Rather, it authorizes the officers who evaluate their applications for things like green cards and residency visas to count the use of these programs against applicants and gives them authority to deny visas on these grounds -- even if the program was used by a family member.

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