The latest effort comes, like previous ones, from lawmakers with ties to Poland. Senator Barbara Mikulski (Democrat, Maryland), of Polish ancestry, is trying to add language to a funding bill that would give the secretary of homeland security the flexibility to grant visa waiver status to allies that share intelligence and cooperate in fighting terrorism.

She wants to replace the existing law that only lets a country join if its visa refusal rate is below 3%. Apart from Poland, Bulgaria,…