Carter declares war on Iran over the hostage crisis. Incumbent presidents during war usually wins
This is extremely out of character for Carter. He was totally focused on the safety of the hostages. Some kind of military option to force the Soviets' hand was not out of the question - as we saw with Eagle Claw. But declaring war on Iran is simply a bridge too far with Carter in the White House.
The only way to get Carter to declare war on Iran is if they kill a hostage, and the Iranians knew this, which is a big part of why they didn't harm the hostages.
Was there any chance that Eagle Claw could have succeeded? And would a successful Eagle Claw help or would it just be a spike in the polls and then it's back to normal (Carter struggling) again after some time?
Kai Bird, who wrote
The Outlier, doesn't think it was possible for success. The more I've read about, the more convinced I am that it was going to fail 8 or 9 times out of 10 - there were too many ways for it to go wrong. That said, there's a timeline out there in which it goes off without a hitch, everything falls together perfectly, and the hostages are rescued.
In order of their importance, there are three main reasons why Carter failed to win reelection. They are:
1. The Economy
2. The Hostage Crisis
3. Ted Kennedy's primary challenge
All three contributed to an image of Carter as an ineffectual president. The path to a Carter reelection is hard, but not at all impossible. Consider the following:
1. The Economy - The Volcker shock devastated the economy in a fashion almost perfectly timed with the 1980 election. There are several ways to get around this. The narrowest POD is that Carter appoints someone else to the Fed Chair spot. Advisers told him that Volcker was going to doom his electoral prospects. Carter wasn't persuaded by this and believed the economy needed Volcker. Carter is a man of paradoxes. He was intensely competitive and wanted to run the hardest campaign necessary, yet at the same time he was unwilling to manipulate presidential decisions to favor his reelection prospects. Carter considered Tom Clausen and was hesitant enough about Volcker that Carter offered Clausen the job. Clausen's wife, Peggy, didn't want to move to DC and so the job went to Volcker when Clausen declined.
Another way around Volcker is to wave off the entire cabinet reshuffle. This is my favored version of events. Without the reshuffle, Carter's dip in the polls in the summer of 1979 is largely avoided and you avoid the opening at the Fed. Rick Perlstein argues that pretty much any other fed chair could've held things together enough to make sure the economy wasn't a total disaster in November of 1980.
2. The Hostage Crisis - The hard part about the Hostage Crisis is you need it for Carter to win the primaries over Kennedy, but you need to avoid it for him to win the general election. There are a number of military options, including a blockade or mining of Iran's ports, or a successful Eagle Claw that allow Carter to get the hostages home. You could hand wave the Crisis away altogether pretty easily - Carter never really wanted the Shah to come here, he could have increased the security around the embassy in the wake of the first hostage taking in February, or Thatcher (or some other world leader) could've offered to take the Shah instead as she almost did IOTL. But again, I think in this scenario, Carter is exceptionally vulnerable to Kennedy's challenge. The Crisis allowed Carter to reframe the primary fight away from the domestic issues where he was out of touch with the base and it also gave him an excuse to stay at the White House while Kennedy traipsed around the country and largely embarrassed himself until the second half of the campaign.
3. Kennedy's primary challenge - The Hostage Crisis and the disastrous Mudd interview happened on the same day. Kennedy announced his campaign (formally) days later. From the outset, Kennedy underperformed. His comments on the hostages backfired spectacularly and it seemed he lost himself votes every time he gave a speech, answered questions in an interview, or campaigned somewhere in the country. He lost badly in Iowa and New Hampshire - the NH defeat is especially embarrassing given the fact the state almost always goes to the candidate who lives nearest to it (Sanders in 20 and 16, Clinton in 08, Kerry in 04, Tsongas in 92...). All of this is to say, New York looked like the moment Carter would knock Kennedy out of the race altogether. Had Kennedy lost here, it's very hard to see him continuing and while it's easy to say "A Kennedy would never have dropped out!" Jon Ward in
Camelot's End posits that's exactly what Kennedy was planning had he lost NY.
Carter lost NY largely because he pissed off the Jewish bloc of voters there. Of course a lot of things precipitated this. One was Andrew Young's meeting with the PLO in August of 1979. The second was when Young's replacement voted in favor of a resolution that condemned Israeli settlements. Carter asked McHenry to vote in favor of the resolution IF it didn't include any mention of Jerusalem. The preamble of the resolution still included mention of Jerusalem but McHenry voted for it anyway. Leaders in the American Jewish Community argued that this raised doubts about Israel's stewardship over the Holy City. This was not Carter's intent nor his administration's policy but McHenry's vote raised doubts. Instead, had McHenry demanded the language been removed as Carter had asked, and if the authors kept it in anyway and he instead abstained, the whole kerfuffle could've been avoided. That would likely have been enough for Carter to hold on to just enough of the Jewish vote to win the NY Primary, and therefore knock Kennedy out of the race. With Kennedy out earlier, the Convention can be a unifying experience targeted at Reagan instead of filling Democrats with a sense of buyer's remorse.