Washington (CNN) US allies campaigning hard in the halls of Congress to preserve the Iran nuclear deal are finding the process frustrating and confounding.

In conversations with CNN, some foreign diplomats and officials who back the deal say that at the highest levels, the White House has seemed at times so wedded to its talking points on Iran that it doesn't listen, with President Donald Trump stuck in "transmit rather than receive mode."

The State Department, they say, isn't really part of the conversation.

"The ball really is with Congress right now," so that's where diplomats have been focused, said one senior official, but even there, things aren't going all that well.

Some say animosity between Republicans and Democrats has made their work uncomfortable. And while all the officials CNN spoke to said lawmakers are avid for input from allies, some worry that Congress' attempts to fix the deal will spin out of control and ultimately drag the Joint Comprehensive Plan of Action down with it.

'Not about banging down doors'

US law gives Congress some oversight of the Iran deal, allowing it to slap sanctions on Tehran if lawmakers don't think it's complying. But the White House wants Congress to toughen its oversight by amending a law called INARA, so that the US can potentially sanction Iran for activities that were never part of the nuclear deal in the first place. The alternative, Trump has threatened , is that he'll walk away from the deal. The danger of amending the law, some European diplomats say, is that Iran will see this as a violation of the international agreement.

"There are lots of well-intentioned people on both sides in Congress," said one European diplomat. "Our worry is, once you start tweaking INARA, you could end up essentially renegotiating the deal unilaterally, and then you lose control of it if Iran ultimately walks away."

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Diplomats whose countries back the deal estimate that their teams have held dozens of meeting on Capitol Hill in the past few months. In the last two weeks, senior European officials, including EU foreign policy chief Federica Mogherini and UK Foreign Secretary Boris Johnson, have also descended on the Hill.

One diplomat from a country that supports the deal said the point isn't to lobby Congress but to say, "Here's why we feel the way we do." It's not about banging down doors, this diplomat said, but about working with Congress.

Israeli and Gulf officials quietly make their case in meetings with lawmakers and administration officials. At lower levels, Washington-based diplomats have pressed the issue on the Hill and at the White House for months in an effort to influence whether the deal should change, and to what degree.

Israel argues the deal should be "fixed or nixed," while Gulf countries say it should be toughened and used to pressure Iran. Countries that support it, on the other hand, say trying to reopen the international pact would unravel it, undermining global security. The deal, reached in July 2015 , was negotiated between Iran, Russia, China, the US, France, Germany, the UK and the European Union.

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Diplomats on all sides of the deal have focused their tug-of-war campaign on Capitol Hill since October. That's when Trump -- hostile to the nuclear deal but stymied by declarations that Iran is complying from the United Nations, US allies and even his own national security staff -- punted the issue to Congress.

Before Trump handed it off to Congress, some supporters of the deal say, they were having a tough time getting their message across to the White House. When British Prime Minister Theresa May met the President in New York in September, the first issue she raised was the nuclear deal, and she came away with the sense that he wasn't really listening, according to someone present who spoke on condition of anonymity to discuss the meeting.

'Transmit, rather than receive mode'

That person said Trump kept interjecting with simple talking points -- "It's the worst deal ever" -- without explaining his reasons or addressing the substance, while the Prime Minister wanted to focus on the details of the deal, stress that Iran was in compliance and convey that the UK would work with the US to ratchet up pressure on Iran for its other malign activities.

Afterward, the person present said Trump had clearly been "on transmit rather than receive mode."

In contrast, lawmakers from both parties are reaching out to engage on the substance, foreign diplomats said. Those involved with amending INARA are telling diplomats from allied countries that their goal is to keep the US compliant with the nuclear deal.

"I got clear indications that the intention is keep the United States compliant with the agreement and find ways to do that in coordination with ... the European Union, as such, and the rest of the international community," Mogherini said.

The EU's top diplomat was speaking to the press during a break in her 24-hour blitz through Congress over Nov. 6 and 7. But Capitol Hill dynamics are leading some advocates for the deal to pull back a bit.

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"The Republicans are saying, 'We have been asked by the President to find a solution, so please help us,'" said one diplomat. "On the other side, the Democrats said to us, 'Don't help this President.' We don't want to be involved in a national battle," the diplomat continued, saying that their country is keeping tabs on the situation but is no longer actively campaigning. "We don't want to be caught in the middle."

Foreign officials who are staying steadily engaged with lawmakers say they often encounter misunderstandings about the pact and what it does. "They all think they know," said one official. The complexity of the agreement makes it easy to sell certain angles to people with influence but provides little time to deeply study the matter, these foreign diplomats said.

Mogherini, in her remarks to the press last week, expressed some frustration about this, saying the deal was the result of "12 years of negotiations ... resulting in 104 pages of extremely detailed provisions. Most of us in this room would have difficulties, let's say, decrypting in some parts, even if we've all developed a certain knowledge and skill when it comes to centrifuges and heavy water."

A major bone of contention is the so-called sunset clauses that allow Iran to start developing advanced centrifuges and bolstering its uranium enrichment after a few years. Critics of the agreement, such as Israel, say this will facilitate Iran's eventual development of a nuclear weapon, a view many lawmakers hold.

Getting it past the White House

Mogherini stressed the EU line: The deal doesn't facilitate Iran attaining a nuclear weapon, because under it, Iran explicitly commits never to develop a nuclear weapon. "The commitments not to develop nuclear weapons are forever," she said.

One diplomatic source said Republicans "think it's going to be a free-for-all once the sunset comes," but added that "that's not the way the deal works, that's not true." But this official said that even when Republican lawmakers accept that the law isn't as simple as they're making it out to be, they remain fixated on using INARA to make things tougher because that's what the White House demands.

Lawmakers are considering amending the law to include clauses on Iran's missile use , the sunset clauses and ballistic missile development that would trigger more sanctions to rein in malign Iranian behavior in Lebanon, Syria and elsewhere. Iran's ballistic missile program isn't covered by the nuclear deal, but it is forbidden by the UN resolution that endorsed the pact.

Senior diplomats say they have explicitly explained what they see as the danger of this approach to members of Congress: that putting in these "triggers" to increase sanctions on Iran could backfire.

"But they say if they don't have something in there like that, the President will just throw it out," said the diplomat. Lawmakers on "both sides say they need something, to get it past the White House."

"They say, 'Work with us: Let's find language that will warn Iran, but keep the deal,'" the diplomat said. "But the huge question mark for us is, is that even possible?"