That proposal, which had backing from Senator Marco Rubio of Florida, helped torpedo Mr. Rubio’s 2016 presidential campaign and served as the focal point of attacks from conservatives including Jeff Sessions, who would eventually serve as a key surrogate and attorney general for Mr. Trump.

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Homeland Security officials in the Trump administration have said that plans like Mr. Sanders’s, which would forgo deportations for any undocumented immigrant who has been in the country for at least five years, could serve as a magnet for migrants from around the world, many of whom would have little trouble avoiding detection for that time.

Unlike Republicans, Democrats have not made immigration policy a front-burner issue on the presidential campaign trail. The leading candidates all agree in their staunch opposition to Mr. Trump’s immigration policies, with the border wall and family separation policies drawing particular ire.

But in Iowa, where Democrats will hold the party’s first nominating contest on Feb. 3, immigration policy has not drawn nearly as much attention as the debate over how to expand health insurance coverage, which has created a stark contrast between Mr. Sanders of Vermont and Senator Elizabeth Warren of Massachusetts on one side and former Vice President Joseph R. Biden Jr. and Mayor Pete Buttigieg of South Bend, Ind., on the other.

Ms. Warren has called for some of the same immigration priorities as Mr. Sanders, including decriminalizing the border. Mr. Biden and Mr. Buttigieg have not offered detailed immigration plans and have not specified how they might change deportation policies.

Chris Newman, the general counsel for the National Day Laborer Organizing Network, a pro-immigration group, said the Sanders proposal was the “gold standard” of progressive immigration proposals in the 2020 field.