President Barack Obama’s efforts to cement the nuclear deal with Iran hinge on support from a majority of senators in his party, many of whom face competing political pressures as they weigh an agreement that could reshape the U.S. relationship with the Middle East.

Sen. Chuck Schumer of New York, the chamber’s Democratic leader-in-waiting, is perhaps the most closely watched, because of his influence in the broader caucus. The top Democrat on the Senate Foreign Relations Committee, Ben Cardin of Maryland, is pivotal because he is a point person for the party on foreign policy, as is Sen. Chris Coons (D., Del.), whose views are being solicited by others in the caucus.

So far, few of the Democrats have shown their hand as they assess the deal, its likely impact on the Mideast—and on their own political futures. Even Minority Leader Harry Reid (D., Nev.), who isn’t running for re-election and is often a reliable Obama ally, is a question mark...

...The White House faces additional uncertainty with lawmakers such as Sens. Kirsten Gillibrand of New York, Cory Booker and Bob Menendez of New Jersey and Bill Nelson of Florida, who face pressure because of large Jewish populations in their states.

The tone from the New Jersey Democrats hasn’t been not promising for the White House. “I’m concerned that the deal ultimately legitimizes Iran as a threshold-nuclear state,” Mr. Menendez said in a statement this week. “The bottom line is: The deal doesn’t end Iran’s nuclear program—it preserves it.”

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