Ms. Pelosi has not said whether she would support the bill if it passed the Senate, and a spokeswoman declined to comment. A House leadership aide, speaking on the condition of anonymity because he was not authorized publicly, said the bill was likely to draw extended scrutiny in House committees before — or if — it was ever considered on the floor.
It is not clear how Ms. Omar and other progressives would vote on the measure, although similar efforts have attracted opposition on the basis of objections by the American Civil Liberties Union and progressive Jewish groups.
“This legislation appears designed less to combat anti-Semitism than to have a chilling effect and to crack down on campus critics of Israel,” Jeremy Ben-Ami, the president of J Street, a liberal advocacy group that has been sharply critical of Israel’s government under Prime Minister Benjamin Netanyahu, said in a text message.
“It’s misguided to legislatively declare a broad range of nonviolent campus criticism of Israel as anti-Semitism, especially at a time when the prime driver of anti-Semitism is the xenophobic, white nationalist far-right,” he said. “This bill is part of a cynical effort by some of its right-wing proponents to turn the issue of anti-Semitism into a partisan political weapon.”
But in the past, the bill has had widespread support among lawmakers in both parties, and it has the backing of Aipac and the Anti-Defamation League. It also has the support of a powerful outside advocate: David Krone, the hard-driving former chief of staff to Harry Reid, the former Senate Democratic leader, who has used his contacts in the party to push the measure for several years in response to a wave of anti-Semitism on college campuses.
“I find great irony in what Congresswoman Omar said about the issue of Jews and dual loyalty,” Mr. Krone said in an interview. “I am certain that she found the whole birther movement disgusting, vile and flat-out racist. I agree. It was abhorrent to question the loyalty of President Obama. But how, on one hand, can she say it is wrong about people questioning President Obama’s loyalties, but on the other hand, question mine as a Jew? What she said and what some stupid birther said are equally idiotic.”
Ms. Omar’s spokesman did not immediately return a request for comment.
Top Democrats are hardly ready to cede support of Israel to Republicans. Representative Steny H. Hoyer, the Democratic leader, gave a rousing defense of the American-Israeli relationship at the Aipac conference Sunday evening, promising to push for a resolution that opposes the boycott Israel movement. Without naming her, he took several jabs at Ms. Omar.