Ilan Goldenberg, a former top State Department official who worked on the Israeli-Palestinian peace process, said Mr. Netanyahu’s tactics in the fight against the Iran deal — including a formal speech to a joint session of Congress railing against it — had permanently alienated some liberal Democrats.

“Those people are never coming back to him,” Mr. Goldenberg said. “Then there are the folks who are looking for a way back — they want this over, they want this done with, they want to be supportive of Israel without all these tensions and difficulties, and they don’t want to be put in this position again.”

Both sides view the meeting between Mr. Obama and Mr. Netanyahu as a chance to make that happen. Included in their talks will be discussions on a new, larger United States security assistance package for Israel, something that lawmakers in both parties enthusiastically embrace.