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But now, whenever he wonders if he’s on the right track, he thinks about his son, De’Mauri, who just turned 2 this spring.

Matteo Mauri, a lawmaker with the opposition Democratic party, estimated that the accord would cost Italy 653 million euro — about $700 million — in the first five years, for what he said was a negligible number of migrants.

“Not only is the accord completely useless and of dubious legitimacy according to European Union legislation,” Mr. Mauri said, but it is also “immensely costly.”

With European elections looming in June, Mr. Mauri called the deal an “operation of political propaganda by the prime minister” who has made curbing migration a political cornerstone of her party, the hard-right Brothers of Italy.

Those flyers were about a man who lived nearby, on West 70th Street: Joe Mauri.