Iran and the US aim in talks starting from Sunday in Switzerland to begin closing in on a deal reducing Tehran's nuclear activities to within strict limits after 18 months of tortuous negotiations.
Time is however running short and tempers are fraying in Washington where critics fear that the mooted accord will not do enough to prevent the Islamic Republic getting nuclear weapons.
US secretary of state John Kerry, due to meet his Iranian counterpart in Lausanne later, sought to allay such concerns, saying the aim was "not just to get any deal, it is to get the right deal".
The target is for Iran and six world powers -- the US, Russia, China, Britain, France and Germany -- to agree the outlines of a deal by March 31 and to fine-tune the details by July 1.
Kerry said Saturday that his "hope" is that the deal can be clinched "in the next days". But he cautioned that there remained "some important gaps" between the two sides.
"We believe very much that there's not anything that's going to change in April or May or June that suggests that at that time a decision you can't make now will be made then," Kerry told CBS television.
If Iran's nuclear programme is indeed "peaceful," as Tehran says, "let's get it done," Kerry said.
The United States and Iran have not had diplomatic relations for 35 years and the standoff over Tehran's nuclear programme has dogged its international relations for more than a decade.
But the 2013 election of President Hassan Rouhani resulted in a minor thaw and the past 18 months have seen an intense diplomatic effort to resolve the issue.
Under a landmark November 2013 interim deal, Tehran stopped expanding its activities in return for minor sanctions relief. Since then the parties have been pushing for a lasting accord.
But to the alarm of Israel and US Republicans, Washington looks to have abandoned insisting that Iran dismantles all nuclear activities, tolerating instead a small programme under tight controls.
In theory, this still leaves Iran with the possibility to get the bomb, critics say, and last week 47 Republicans took the unprecedented step of writing an open letter to Iran's leaders.
They warned that any nuclear deal could be modified by Congress or revoked "with the stroke of a pen" by whomever succeeds President Barack Obama, a Democrat.
This followed a barnstorming address to US lawmakers -- on a Republican invitation -- by Israeli Prime Minister Benjamin Netanyahu warning against a deal.
Republicans have also threatened to bring draft legislation imposing more sanctions towards the end of March, something which would likely prompt Iran to walk away.
The letter provoked a storm in Washington with Vice President Joe Biden calling it "dangerous" and the State Department saying it was "harmful to American security."
Obama said in a Vice media interview to be released Monday that he was "embarrassed" for the signatories, while Washington's allies in its talks with Iran were also unimpressed.
"The negotiations are difficult enough, so we didn't actually need further irritations," German Foreign Minister Frank Walter Steinmeier said.
And Iranian Foreign Minister Mohammad Javad Zarif, due in Lausanne on Sunday -- and in Brussels on Monday to meet his British, German and French counterparts -- said it "told us that we cannot trust the United States."
No third extension
Some progress has been made towards a final deal but the two sides remain far apart on several key issues.
These include the future size of Iran's uranium enrichment capacities -- which can make nuclear fuel but also the core of a bomb -- the pace at which painful UN, US and EU sanctions would be lifted and the accord's duration.
Two deadlines, in July and November, passed without an agreement but in view of the controversy in Washington -- and pressure in Iran on Rouhani to deliver -- extending yet again will be very tough.
"There is no time for additional extensions," said Kelsey Davenport, an analyst at the Arms Control Association.
"After March, it becomes much more difficult to hold off legislative attempts by Congress to sabotage the deal," Davenport told AFP.
Iran's supreme leader, Ayatollah Ali Khamenei, has meanwhile criticised the two-step process, saying matters should be handled in one fell swoop.
Khamenei is due to give a closely watched Iranian New Year's address on March 21. Last week he said the other side in the talks was "deceitful and stabs in the back".