Striking a compromise is one of the most perilous moments for a leader because it involves sacrificing maximalist goals to offer terms that can be accepted by former enemies.
The resulting feelings of intense disappointment among followers who had been led to believe in total victory, or the ability to avoid painful concessions, can produce a sense of bitterness, leading to rejection of the deal and even the leader's replacement with a more uncompromising figure.
But sometimes compromise, even betrayal, are necessary to break the status quo and permit an organisation or system to evolve.
This is essentially the problem both the Obama administration and the Iranian leadership confront in reaching a final settlement, or at least a durable long-term agreement, over Iran's nuclear program.
Neither U.S. President Barack Obama nor Iran's Supreme Leader Ali Khamenei is personally at risk. Their constitutional authority and personal prestige respectively are too strong.
But their chief negotiators - U.S. Secretary of State John Kerry and Iran's President Hassan Rowhani and Foreign Minister Mohammad Javad Zarif - have invested substantial personal and political capital in the talks process and would be badly damaged if it falls apart.
Now they must persuade sceptical domestic audiences that a flawed deal is better than none at all.
The main bargaining elements for a final settlement are known: the extent to which Iran will be permitted to maintain its ownenrichment program versus the extent to which sanctions will be lifted and the country's international relationships will be normalised.
In that sense, the zone of possible agreement (ZOPA), as it is known in sales negotiations and bargaining theory, is well understood by all the diplomats involved in the process.
There is some scope for creativity.
The two sides could try to reach a "grand bargain" in which Iran ends all enrichment in exchange for the full lifting of sanctions and complete normalisation of its international relations. Or they could strike a more limited deal leaving Iran with some enrichment and subject to certain restrictions on its trading position.
Other options include capping the number of centrifuges and the amount of uranium Iran can enrich at home, perhaps to the amount needed to run one or two civilian power reactors, coupled with an agreement that the country will import enriched uranium in the form of fabricated fuel rods if it decides to build any more reactors.
The real challenge for diplomats on both sides is to gauge how far they can go in making concessions before they lose support at home, and to use the period of the talks to soften public opinion for an eventual deal.
The Obama administration must face down the many hardline politicians and foreign-policy experts in the United States, Israel and other Middle East allies who believe sanctions are working and will eventually force the Iranian leadership to dismantle the nuclear program without conditions.
In Iran, the nuclear negotiators must convince the country's hardliners that accepting restrictions on enrichment and the nuclear program will leave Tehran's international position more secure, and bolster rather than undermine the government's position domestically.
If the final deal leaves Iran with significant enrichment capability, which seems likely, it will bitterly disappoint U.S. hardliners who believe Tehran can be compelled to climb down through the application of economic pressure.
"The perplexing thing about the Obama administration's recent diplomacy about Iran: Messrs Obama and Secretary of State John Kerry don't seem to recognize that they will likely never again have as much economic leverage over Tehran as they do now," Mark Dubowitz, executive director of the Foundation for Defense of Democracies and a leading sanctions proponent, wrote in the Wall Street Journal ahead of the agreement.
"The efficacy of sanctions depends on the threat of escalation, where an ever-expanding web of restrictions scares off foreign businesses," Dubowitz explained ("The case for stronger sanctions against Iran," WSJ, Nov. 10).
"Even when sanctions on Iran were violated, that didn't really matter, because Washington - Congress really - created an impression that it intended to circle Iran with an economic minefield."
For escalationists, any relaxation of the economic pressure is a serious mistake. After the joint action plan was announced, Dubowitz described it as a "flawed interim deal (that) may result in an even worse final agreement".
Hawks are unlikely ever to be persuaded by the White House strategy. But the Obama administration must convince sceptics in the U.S. Congress, as well as ordinary American voters, and its allies in the Middle East, that the alternative is not victory through sanctions but a defiant and nuclear-capable Iran. It could prove a tough sell.
Far from normal
Iran too will have to make some uncomfortable compromises. The United States will not grant Tehran the recognition as a regional power that it craves, or guarantee the survival of the Islamic Republic's political institutions.
The United States and its allies will still want to alter Iran's internal governance even if there is no formal policy of regime change.
Any final deal will almost certainly involve severe restrictions on the number of centrifuges and the amount of uranium that can be enriched, leaving the country far short of the complete fuel cycle and nuclear self-sufficiency Tehran says it needs.
Certainly, Iran will not be allowed to operate enough centrifuges to fuel a whole string of civilian nuclear reactors because the proliferation risk would be too high.
Iran will be subject to a far more intense level of inspections by the International Atomic Energy Agency than any other country. The price of easing sanctions is that Iran will be put "on probation" for years.
The objectives of Iran's nuclear program are disputed. But if the strategy revolves around creating the capability to build a nuclear weapon, if not actually building one yet, intensive inspections plus restrictions on the volume and level of enrichment would make that much harder to achieve in the short term.
The length of time needed to "break out" and build a weapon plus a reliable delivery system would increase, and it would be much harder for Iran to build a bomb undetected.
Rowhani and Zarif must convince enough members of the political elite, especially the supreme leader, that the loss of security that comes with restrictions on enrichment is more than offset by gains from a lifting of sanctions and a revitalization of the economy.
Less than perfect
The talks in Geneva are straightforward compared with the complexity of the negotiations that each side must conduct domestically.
Hardliners in Washington and Tehran will reject any deal. The task for Obama and Rowhani is to isolate them by convincing enough skeptics and waverers that an imperfect compromise is preferable to pursuing an ideal outcome by escalating confrontation.
But it is a delicate process. Many Americans who believed Iran could be forced to yield through sustained pressure must be convinced to accept Iran will retain some enrichment capability ("rewarded for bad behavior", as U.S. hardliners put it).
Iran will have to accept that even after a deal there will remain intense suspicion about its motives, it won't get full security guarantees, and it will still not be treated by the United States, Washington's allies, and Gulf neighbors as a normal country.
The next six to 12 months will test the sales skills of leaders in both countries as much as their negotiating ability.