Nearly 200,000 children across Florida could lose their automatic access to free school lunches under a Trump administration proposal that would limit the number of people enrolled in the federal food stamps program, formally known as SNAP. The proposal — first announced in July by the United States Department of Agriculture — would restrict SNAP enrollment by taking away states’ ability to tweak some income and asset limits for households that receive both food stamps and other welfare benefits. In Florida, that flexibility had allowed the state’s Department of Children and Families to raise the threshold for SNAP qualification, letting households with incomes up to 200 percent of the poverty level receive food stamps — among the highest in the nation. Under the stricter eligibility criteria imposed in USDA’s proposal, 328,000 Floridians, and three million people nationwide, would see their Supplemental Nutrition Assistance Program benefits end. Children would be among the hardest hit because SNAP participation also grants them automatic access to free school lunches, a provision that’s part of the USDA’s National School Lunch Program. In Florida, the number of kids that would be subject to losing both their food stamps and their automatic eligibility for free lunches at school stands at 195,888, with some counties affected more than others. Among the places where the policy change could take a big toll is Miami-Dade, where 71 percent of the student body is enrolled in the National School Lunch Program. That’s the fifth-highest percentage in the state, according to the nonpartisan Florida Policy Institute.