WASHINGTON — In its delicate negotiations with Iran over freezing its nuclear program, the Obama administration is gambling that the gradual relaxation of punishing sanctions will whet Tehran’s appetite for greater economic relief, inducing the country’s leaders to negotiate a further deal to roll back its nuclear progress.

Yet, President Obama’s biggest critics — in Congress, the Arab world and Israel — argue that he has the strategy entirely backward. By changing the psychology around the world, they argue, the roughly $100 billion in remaining sanctions will gradually be whittled away. Wily middlemen, Chinese eager for energy sources and Europeans looking for a way back to the old days, when Iran was a major source of trade, will see their chance to leap the barriers.

Secretary of State John Kerry arrived in Geneva Saturday for his second visit in two weeks, again heightening expectations that negotiators are close to agreement on a pact to suspend Iran’s nuclear program for six months. But Mr. Kerry cautioned that his presence and that of the five other foreign ministers whose countries are negotiating with Iran might not be enough to guarantee that a deal could be reached.

Nevertheless, with a deal seemingly in reach, the focus is now shifting to the details, and particularly what sanctions would be reversed, in return for the freezing or dilution of Iran’s uranium stockpile.