More than a dozen of the 34 Democratic senators who have declared their support for the Iran nuclear agreement cited arguments by America’s five negotiating partners that there would be no better deal forthcoming if the U.S. rejects this one.

On Wednesday, the number of senators to have publicly stated support for the Joint Comprehensive Plan of Action (JCPOA) climbed to 34 – all Democrats – thereby giving President Obama the backing he needs to sustain his veto of a Republican-led resolution disapproving it, which is expected to pass by mid-September.

As previously undecided senators one by one came out in support of the agreement over the past month, references in their statements to the views of the other P5+1 governments involved in the negotiations – Russia, China, Britain, France and Germany – were strikingly common.

Many of them attended a briefing by ambassadors from those countries in early August.

When she announced her support for the deal on August 6, Sen. Kirsten Gillibrand (D-N.Y.) said, “In a meeting earlier this week, when I questioned the ambassadors of our P5+1 allies, it also became clear that if we reject this deal, going back to the negotiation table is not an option.”

Four days later Sen. Amy Klobuchar (D-Minn.) said she had asked the ambassadors of the five other countries involved in the talks “detailed questions about what their countries and others would do if Congress does not approve the agreement.”