Iran and the United States negotiate in what political scientists call a two-level game. The executives of both countries negotiate with each other, but they also have to negotiate with their domestic forces (and international allies). Domestic actors must approve of any agreement between the leaders.
In such a game, domestic forces have an incentive to act extra critical so that their leaders will have less ability to concede. If Congress demands a hard line, Obama can claim that he can't give into Iranian demands because Congress wouldn't approve those concessions. If the Iranian military insists on an equally difficult stance, the Iranian president will also have little room to move.
While domestic actors may advocate toughness in their negotiations with their leaders in order to give those leaders leverage, they can also ruin the possibility of a deal. Both countries' domestic forces may draw lines that pass each other, leaving no agreement possible. If the pride of the Iranian government and society will not allow Iran's president to give up on any enrichment. Then, the U.S. Congress insisting on no deal except zero enrichment will guarantee no diplomatic solution.
Voices in both countries have announced their concerns with the current first-step deal. Pundits, allies, and politicians in the U.S. claim the deal gives too much and even compare it to Nazi appeasement. While conservatives in Iran accuse their administration of being intimidated and surrendering their nation's rights to the U.S.
U.S. domestic opposition may help ensure the administration stays strong, but if it goes too far, then U.S. domestic forces may push the U.S. to war.