President Trump on Saturday in Ohio, where he backed Troy Balderson, a Republican running in a special election, saying a vote for Mr. Balderson’s opponent was a vote for “open borders.”

WASHINGTON — The Trump administration is advancing a plan to punish legal immigrants for accepting food stamps, public housing and other government benefits they are entitled to — a strategy that appeals to conservatives and could help to galvanize Republican voters before the midterm elections.

The proposed rule first surfaced last year. Last month, the White House Office of Management and Budget published a notice that it was under consideration. A Trump administration official said Tuesday that details of the proposal were still weeks away from being finalized and made public.

But already, the rule could serve as a talking point for Republican candidates seeking to counter an expected wave of Democratic enthusiasm, seizing on President Trump’s claims that immigrants are an outsize drain on American taxpayers.

As drafted, the rule would authorize federal officials to revoke legal resident status from legal immigrants who accept government assistance currently available to them.

It essentially concludes that those immigrants are more likely to become “public charges” — dependent on programs like Medicaid, children’s nutrition aid and even housing and transit subsidies.

Many of Mr. Trump’s supporters — voters who will be key to victories by Republicans in close contests this fall — believe that legal immigration has cost them jobs, depressed wages and forced higher taxes.

Recent studies, however, have found that increased legal immigration has led to higher, not lower, wages. Other studies by social scientists suggest that immigration leads to greater, not lower, productivity in the United States and somewhat lower prices for some goods and services.

A 2016 report by the National Academies of Sciences, Engineering and Medicine found that while first-generation immigrants can be more costly to governments, subsequent generations “are among the strongest economic and fiscal contributors in the U.S. population, contributing more in taxes than either their parents or the rest of the native-born population.”

Such studies are unlikely to convince the president’s most ardent supporters, especially in the face of a barrage of campaign commercials that are certain to be broadcast in the months ahead.

Republicans across the United States have already embraced the president’s hard-line messaging about illegal immigration and crime. They are betting that they will benefit politically the way that Mr. Trump…