If the US Congress does not receive the text by early Friday morning Vienna time -- midnight in Washington -- it makes the approval process longer and potentially more problematic.
But despite this pressure, and almost two weeks of talks in the Austrian capital, it is unclear whether an accord aimed at ending a 13-year standoff can be sewn up at all.
US President Barack Obama held a video conference on Monday with the US negotiators and "reviewed the progress of negotiations to date, and provided guidance" to the team, the White House said.
Building on a framework agreement from April, the deal would see Iran dismantle large parts of its nuclear infrastructure in order to put a nuclear bomb out of reach.
In return, a web of painful sanctions on Iran -- which denies wanting the bomb -- would be progressively lifted once the UN atomic watchdog verified Tehran had fulfilled its promises.
"Never have Iran and its counterparts been this close to a final accord. But success is far from assured... Serious political decisions still need to be made," Iranian Foreign Minister Mohammad Javad Zarif wrote in the Financial Times.
US Secretary of State John Kerry quipped Thursday at the start of a new meeting that they were in "Groundhog Day".
"Hopefully today (Thursday) is the last day," Iranian nuclear chief Ali Akbar Salehi said as he met US Energy Secretary Ernest Moniz.
Difficult issues in what will be a highly complex agreement include working out the pace and timing of sanctions relief and a stalled UN probe into alleged efforts by Iran to develop the atomic bomb.
Iran has also insisted there should be changes to a UN arms embargo and an easing of restrictions on missile sales, a prospect alarming rivals of Iran and allies of the United States in the region.
The goal of the sanctions of getting Iran to negotiate had "long been reached" and arms would help Tehran combat Islamist State extremists -- a common enemy for the US, Iran and Russia.
The foreign ministers of Britain, Germany and France rejoined the talks today, with lower level officials sitting in for the Chinese and Russian ministers, whose return is not yet scheduled.
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