The talks, which have blown through repeated deadlines, extended into Tuesday. Earlier Monday, Iran's chief nuclear negotiator Mohammad Javad Zarif signaled to reporters from his Vienna hotel balcony that there would be no deal Monday.
But a deal could come quickly, as an errant tweet from Iranian President Hassan Rouhani suggested.
It read, "#IranDeal is the victory of diplomacy & mutual respect over the outdated paradigm of exclusion & coercion. And this is a good beginning."
The tweet was later re-posted with the word, "If" at the beginning.
Western diplomats tell CNN the hope is that there will be an Iran nuclear deal some time late Monday or early Tuesday. A senior Iranian diplomat directly involved in the talks said Monday night that "We are very close but not there yet. Let's see what's gonna happen in the next few hours."
Iran has been pushing for any resolution which forms part of a deal to curb its nuclear program including the lifting of an embargo against the sale of conventional weapons and missiles. Russia has supported the move. The United States in particular has been resistant to it.
"Under no circumstances should we relieve pressure on Iran relative to ballistic missile capabilities and arms trafficking," said Chairman of the Joint Chiefs Gen. Martin Dempsey
last week on Capitol Hill.
Despite that declarative statement from the top U.S. general, administration officials and western diplomats tell CNN the issues are not insurmountable, but negotiators still have to unpack all of the details -- and negotiating every word is tedious and takes time.
Western officials have said negotiators made good progress over the weekend and the talks were reaching the "endgame."
Negotiators met Monday in a Vienna conference room after Western diplomats said the major hurdles to a deal had been overcome. Those diplomats also acknowledged some important issues needed to be resolved and capitals still needed to sign off. Those loose ends kept Iranian officials from sounding more optimistic.
"There are two or three things that need to be worked out," a senior Iranian official told CNN on Sunday.
Western officials had hoped for the announcement of a deal Monday.
"We are nearly there," one Western diplomat said.
An Iranian official said whether or not a deal gets struck hinges on the negotiators' appetite for getting it done.
"It only depends on political will," the official told CNN.
Secretary of State John Kerry on Sunday said he is "hopeful" a deal can be reached.
The negotiators, facing another deadline, on Friday extended the talks through Monday. This was the third extension of the final round. The parties also extended the interim agreement, known as the Joint Plan of Action, through Monday.
On Saturday, after one of his meetings with the European negotiator and the Iranian Foreign Minister, Kerry tweeted "Still have difficult issues to resolve."
Several of the European foreign ministers had left Vienna late last week, but have since returned.
French Foreign Minister Laurent Fabius, who just arrived back to the Iranian nuclear negotiations in Vienna, said he was optimistic the talks were nearing completion.
"I hope we are finally entering the final phase of these marathon negotiations," he told reporters, outside the Palais Coburg. "I believe it."
In another signal that talks are entering a critical stage, Russia's Foreign Minister Sergey Lavrov is back in Vienna to join negotiations.
But a senior State Department official cautioned against too much optimism at this stage.
"We have never speculated about the timing of anything during these negotiations, and we're certainly not going to start now - especially given the fact that major issues remain to be resolved in these talks," the official told CNN.