The White House is again considering setting the number of refugees who can enter the United States through September at about 62,500, according to three people familiar with the deliberations, under pressure from immigrant rights groups furious about President Biden’s recent retreat from that target. Less than two weeks after White House press secretary Jen Psaki said Biden intends to announce a new cap for the fiscal year by May 15, but signaled that his original target was no longer realistic, people inside and outside the White House suddenly sound hopeful about landing at or near the number the Biden administration announced with some fanfare in February... The latest machinations follow intense private and public pressure from refugee advocates, who have lashed out at the White House for backing away from its promise. In a private videoconference last week, the heads of resettlement agencies who work with the government vented their frustration with White House aides, according to two people with direct knowledge of the conversation. Ernesto Apreza, a senior adviser for public engagement at the White House, acknowledged during the call that administration officials needed to do a better job of keeping the refugee resettlement groups informed. The White House outreach in recent months “falls very short” of what it should have been, Apreza said, according to a person with direct knowledge of his comments.