But details about enforcement and about constraints on the nuclear program remain to be finalized. CBS News reported on Monday that it remained unclear whether Iran would accept snap inspections of suspicious nuclear and military sites, and whether it would be required to fully comply with an International Atomic Energy Agency probe into the past military dimensions of its nuclear work. It has also not been specified how much advanced nuclear development Iran will be permitted to pursue under the terms of the deal.

The lack of answers on these points continues to fuel speculation about Western powers extending still more concessions to Iran in order to rush an agreement. Senator Bob Corker, the author of a Iran Nuclear Agreement Review Act, which requires Congressional review of any deal signed by the Obama administration, urged Kerry to take the time to see that no further red lines are crossed by Tehran, according to The Chattanoogan.

But this recommendation appears to come in response to the administration’s fear that finalization of the agreement will be made more difficult by its being signed after July 9, at which point Congress will have 60 days to review it, rather than just 30.

At the same time that this gives the Obama administration some incentive to push for a quick deal, Tehran may have its own incentive to draw out the process even further. According to Iran’s semi-official Tasnim News Agency, an Iranian diplomat at the Vienna negotiations declared that Iran does not consider itself to be bound by deadlines and is willing to extend the talks beyond July 9.

On the other hand, there is little doubt that Iran wants to secure a deal quickly if that deal results in the immediate, across-the-board relief from economic sanctions that Iranian negotiators have been pushing for throughout the past several months of negotiations. The Wall Street Journal reported on Monday that Iran was anticipating that the prospect of such relief would result in the doubling of the country’s oil exports, from 1.2 million to 2.3 million barrels per day.

At the same time, Iran is pushing for the re-imposition of OPEC quotas, which contrasts with the desire of Saudi Arabia to maintain or expand its existing market share. Iran’s expanded presence in the oil market could exacerbate conflicts between the Sunni monarchy and its Iranian Shiite rivals. The current proxy conflict between the two players in the Arabian kingdom of Yemen is only one element of the Iranian regional influence that could be affected by some provisions of the nuclear agreement.

American resistance to Iran’s efforts to expand its clout in the Middle East may in fact counteract whatever incentive the Obama administration feels to rush an agreement or provide further concessions. The Associated Press reports that Iranian negotiators are now pushing for an end to US arms embargos on the Islamic Republic, and possibly UN embargos as well. American and other Western officials have been clear in their statements declaring such demands to be unreasonable.

The US recognizes that allowing arms to freely enter Iran would also allow them to be channeled into the hands of the Assad regime in Syria, as well as to various terrorist groups known to be sponsored by Tehran. What’s more, the potential impact of Iranian arms on US foreign policy interests was indirectly highlighted by one of Iran’s highest ranking military leaders in a statement on Sunday. According to the Times of Israel Brigadier General Ahmad Reza Pourdastan, the commander of Iranian ground forces, rejected the notion of overall rapprochement between the two nations, saying, “The US might arrive at some agreements with us within the framework of the Group 5+1, but we should never hold a positive view of the enemy.”

For some critics of the Iranian regime, these sorts of comments raise renewed questions about Iran’s trustworthiness as a negotiating partner. For this reason, many Western commentators have emphasized the need for specifically-outlined mechanisms to respond to Iran’s possible cheating on any deal that is signed in the coming days. On Monday, a Reuters blog post laid out several principles for such mechanisms, particularly underscoring the need for new sanctions to go much further than the existing ones, in order to impose genuine penalties while also making up for Iran’s evasion of and adaptation to the current restrictions.

Of course, such measures are only relevant if a final agreement is in fact signed, and if Kerry is to be believed, that is by no means a foregone conclusion at the current stage. In keeping with other officials’ rejection of the latest Iranian demands, Kerry’s remarks to reporters highlighted Iranian “intransigence” and suggested that if Tehran did not make difficult decisions in a short period of time, the US is prepared to walk away from the deal.

Given what is known about what has been agreed so far, this outcome would be preferable for some critics including Israeli Prime Minister Benjamin Netanyahu, whom CNN quoted as reiterating his consistently harsh assessment of the potential deal. Netanyahu described that deal as being even worse than an earlier agreement between the US and North Korea which resulted in the latter country obtaining a nuclear arsenal.

But participants in the negotiations insist that they still hope to secure a final agreement by the end of Tuesday. An official, months-long extension is reportedly unlikely, but if disputes are still not resolved on Tuesday the seven parties may either walk away from negotiations or continue to unofficially extend the talks by a few days at a time.