For any Democrat anxious to see the unpopular Iran nuclear agreement fade from public view between now and November 2016, it’s been a rough couple of weeks.

Headlines about the GOP Senate’s failed battle to stop the Joint Comprehensive Plan of Action had all but disappeared when Iran launched an Oct. 11 test of an intercontinental ballistic missile. Suddenly foes of the deal were back in the news, accusing Iran of breaking the agreement.

The White House and Iran countered that the launch did not violate the nuclear deal because it does not include missile testing. Even so, a group of Senate Democrats responded with a letter to Secretary of State John F. Kerry denouncing Iran’s move as a violation of U.N. Security Council Resolution 1929 and calling for “unilateral and multilateral responses.”

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“There must be no ambiguity in our willingness to enforce Iran’s obligations under UN resolutions and the JCPOA,” said the Oct. 21 letter signed by 11 Democratic senators.

Only two of those — Sens. Benjamin L. Cardin of Maryland and Charles E. Schumer of New York — voted against the deal.

The episode exemplifies a worst-case scenario for Democrats as they head into next year’s election, namely that Iran will give Republicans ample “I-told-you-so” opportunities by breaking the agreement, violating other international sanctions or keeping the issue in the public eye with recurring acts of aggression or anti-U.S. rhetoric.

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House Committee on Foreign Affairs Chairman Edward R. Royce weighed in after the formal adoption of the nuclear agreement on Oct. 18, known as Adoption Day, by ticking off a list of Iran’s recent transgressions, including Iranian Gen. Qasem Soleimani’s travel to Moscow in violation of sanctions.

“It’s sure tough to look at Iran’s actions over the last three months — let alone 35 years — and think Tehran will live up to its end of the nuclear bargain,” Mr. Royce said in a statement. “If this is what the last 90 days look like, the next few years look like a disaster.”

One day after the long-range missile launch, Iran was hit with more criticism for convicting Washington Post journalist Jason Rezaian on espionage charges, prompting a blast from House Speaker John A. Boehner.

“President Obama’s gamble that a nuclear deal would lead to a more responsible Iran has already failed,” Mr. Boehner said. “This sham of a trial violated every international standard and made a mockery of Iran’s own legal system.”

Senate Republicans, joined by four Democrats, approved a resolution of disapproval Sept. 10 by 58-42 but were unable to muster the 60 votes needed to override President Obama’s veto.

The advocacy group J Street, which ran ads in favor of the nuclear deal leading up to the Senate vote, agreed that the ICBM test was a “gratuitous violation of a U.N. Security Council Resolution” but insisted that it did not breach the JCPOA itself.

“It’s not surprising that groups who oppose the JCPOA are seeking to cast every instance of Iranian bad behavior as a violation of it,” said J Street Vice President of Government Affairs Dylan Williams. “It would be much better for U.S. and Israeli security if those still hoping to kill the deal pivoted to working with the U.S. government to ensure its strict implementation.”

There’s little indication, however, that opponents of the JCPOA intend to back off given the enormous media and political campaign waged over the summer in an effort to defeat the agreement, which lifts economic sanctions on Iran in exchange for restrictions on its nuclear capability.

Opponents like the American Security Initiative and Citizens for Nuclear Free Iran outspent supporters like J Street as of Sept. 4 by a margin of $13 million to $2 million, according to The Wall Street Journal, citing Kantar Media.

Michael Pregent, executive director of Veterans Against the Deal, said his organization is weighing the possibility of more ads tied to the ICBM launch even before the election season gets underway.

“We’re contemplating putting something out talking about these violations,” said Mr. Pregent. “We’ll definitely be getting these up before implementation during the presidential election. We’ll highlight Iran’s violations. If the last 90 days are any indication of what Iran plans to do over the next 15 months, then we know that it’s not going to be a good year.”

The National Iranian American Council said on its blog that recent events may represent an initial response to the deal by Iranian “hardliners digging in” over “trepidation with shifting events while foreshadowing a continued struggle over Iran’s direction,” not a sign of things to come.

“This was far from unexpected, as many observers predicted an initial hardening as factions seek to balance against the success and popularity of [President Hassan] Rouhani and his team,” said the Oct. 16 post.

Even so, Mark Dubowitz, executive director of Foundation for Defense of Democracies, said the ICBM test has direct implications for Iran’s compliance with the deal, which is aimed at preventing Iran from developing nuclear weapons.

“Iran is already in violation of the key U.N. Security Council Resolution (1929) that prohibits the development and testing of ballistic missiles capable of carrying a nuclear warhead,” Mr. Dubowitz said.

“This prohibition extends to the new USCR (2232) that will come into effect after Iran has complied with its nuclear commitments and that also gives effect to the JCPOA,” he said. “To permit Iran to develop with impunity one of the key elements of the nuclear trinity (ballistic missile, warhead, weapons-grade uranium) is to run a grave risk that Iran will continue on the path to the development of an atomic weapon.”

Adam Turner, general counsel and legislative affairs director at the Endowment for Middle East Truth, said the JCPOA’s actual prohibitions are still something of a moving target given reports that the Iran parliament approved an amended version earlier this month.

In addition, the official JCPOA is “very ambiguous, so it is hard to tell if even that is violated,” Mr. Turner said.

Certainly Republicans see the agreement as a winning issue given the polling prior to the Senate vote. A Pew Research Center poll released Sept. 8 found that those approving of the deal had fallen to 21 percent, with 49 percent disapproving.

“The Iran nuclear agreement is likely to be one of the major issues in 2016 because foreign policy has a Republican advantage,” said Denver political analyst Floyd Ciruli, “and they intend on highlighting it.”