The Iranian nuclear talks just went into double overtime - and they're now set to miss a key deadline for Obama

Negotiators in Geneva are set to blow past another deadline in the ongoing discussions surrounding Iran's nuclear program.

And the new deadline could mean more trouble on the domestic front for President Barack Obama.

Iran and the so-called P5+1 - the US, China, France, Russia, the United Kingdom, and Germany - have now given themselves until July 10 - three more days - to work out a final deal.

"We're frankly more concerned about the quality of the deal than we are about the clock," State Department spokeswoman Marie Harf said in a statement. "Though we also know that difficult decisions won't get any easier with time - that is why we are continuing to negotiate."

The new deadline of July 10 is significant, at least for Obama and his team of negotiators, because the real deadline in the final round of talks has been July 9.

That's the day they need to have a deal in order for it to move swiftly through Congress.

Under a compromise bill supported by bipartisan majorities in Congress that Obama signed into law, a 60-day congressional review period on the final deal was cut in half to 30 days.

But that review period will snap back to 60 days if Obama submits the agreement to Congress later than July 9.

Bloomberg's Josh Rogin recently reported that Colin Kahl, Vice President Joe Biden's national security adviser, told an audience at a conference in Washington last month that the administration was operating as if the deadline is July 9.

That stance has raised the alarm of some critics of the negotiations.

"The fact that the Obama administration is so loathe to give Congress an extra 30 days to review what will be the most consequential national security agreement of the post-Cold War era is remarkable," Mark Dubowitz, executive director of the Washington-based Foundation for Defense of Democracies, told Business Insider.

"It tells you everything you need to know about how concerned the administration is to have a serious debate on the actual deal and its consequences."

Reaching a deal by July 9 would mean Congress would have to vote to approve or disapprove the deal before it leaves Washington for its August recess. If the administration can't submit the deal until later in July, it would provide Congress some leeway - likely until September, after its month-long summer break.

The lengthy debate could mean louder opposition when members of Congress return home to their districts in August, with the potential to sway public opinion and, in the end, votes over a final deal.

There's also a concern that Iran could use the deadline - which is far more important to the US than Iran - as leverage to extract further concessions. Russian Foreign Minister Sergei Lavrov hinted Tuesday that there might be a push for the United Nations to completely lift its arms embargo on Iran.

"There is only one big problem in terms of sanctions," Lavrov told reporters. "It is the problem of a weapons embargo."

The run-up to a potential deal has run into opposition from everyone from Republican members of Congress to former members of the Obama administration, who wrote a letter to the president outlining their concerns last week. In a press conference last week, Obama said he wouldn't hesitate to walk away from "a bad deal" if Iran's leaders stick to some of their recent bluster.

"There has been a lot of talk on the other side from the Iranian negotiators about whether, in fact, they can abide by some of the terms that came up in Lausanne," Obama said.

"If they cannot, that's going to be a problem - because I've said from the start I will walk away from the negotiations if, in fact, it's a bad deal. If we can't provide assurances that the pathways for Iran obtaining a nuclear weapon are closed, and if we can't verify that, if the inspections regime - the verification regime is inadequate, then we're not going to get a deal. And we've been very clear to the Iranian government about that."

The Iran negotiations will prove to be a defining part of Obama's foreign policy legacy, geopolitical expert Ian Bremmer, the president of Eurasia Group, recently told Business Insider. The deal has the potential to both radically reshape Iran's role in the Middle East and its relationship with the West, including the US. Potential cooperation with Iran looms on issues like fighting the Islamic State, but closer ties with Iran would also lead to complications with key US allies.

If a deal with Iran is ultimately struck, it'll be a big part of Obama's legacy - but one Bremmer said has become tough for the president to sell as positive. And it will only become more of a lightning-rod issue in Congress if negotiators miss the July 9 deadline.

It "will be extremely controversial in Congress and among key US allies in the region (Saudi Arabia and Israel have good reason to hate it). So I think it will be challenging for Obama to sell that as effectively as positive for his legacy," Bremmer said.