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The White House has threatened to veto any such measure which could harm U.S. relations with Arab states.

The Obama administration is also facing questions about a possible drop in Jewish support after the loss of former Rep. Anthony Weiner's (D) seat in a New York special election last week.

Former President Bill ClintonBill ClintonWhat to know about Trump's national monuments executive order Larry Summers: Mnuchin squandering his credibility with Trump tax proposal Patagonia threatens to sue Trump over national monuments order MORE (D) suggested that voters' fears for Israel's security led to the Democratic defeat in an interview on ABC's "This Week" on Sunday morning.

"I think, Mayor Koch had a big impact on that election because of the controversy surrounding Israel and how they're reacting to the proposal of the Palestinians to get the U.N. to recognize them as a state. I think that had a lot to do with it," said Clinton.