A leading Republican critic of the Iranian nuclear talks is calling on the U.S. to "walk away" from the table after negotiators missed a key deadline, while other lawmakers joined in voicing concern that Iran could extract critical final-hour concessions in the scramble to salvage an agreement. 

Negotiations resumed in Switzerland on Wednesday but were almost immediately beset by competing claims, just hours after diplomats abandoned a March 31 deadline to reach the outline of a deal and agreed to press on. And as the latest round hit the week mark, three of the six foreign ministers involved left the talks with prospects for agreement remaining uncertain. 

Amid the confusion, Sen. Tom Cotton, R-Ark., told Fox News he's concerned the framework of a deal could allow Iran keep its uranium stockpiles and continue to enrich uranium in an underground bunker. 

"You have to be willing to walk away from the table and to reapply leverage to Iran," Cotton said. "And the fact that they're not willing to do that, that we're still sitting in Switzerland negotiating when three of our negotiating partners have already left just demonstrates to Iran that they can continue to demand dangerous concessions from the West." 

Speaking on MSNBC, former Democratic presidential candidate Howard Dean seemed to agree. He said that while President Obama is "right" to seek a deal, it might be time to "step away" from the table and make clear that the U.S. is not backing off key positions -- including on Iran's uranium stockpile and the pace of sanctions relief. 

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"I am worried about this," Dean said. 

Rep. Martha McSally, R-Ariz., also told Fox News "we're potentially [legitimizing] them having a nuclear infrastructure." She added: "We don't know exactly what's behind closed doors." 

Despite all sides agreeing to blow by their deadline in pursuit of a rough agreement, even the White House threatened to abandon the talks if Iran wouldn't budge. 

"If they're unwilling to make those kinds of commitments that give us that assurance -- and by us I mean not just the United States, I mean the international community -- then we'll have to walk away from the negotiating table and consider what other options may be available to us, and there is certainly the possibility that that could happen," White House Press Secretary Josh Earnest said Tuesday. 

Earnest indicated Wednesday that's still an option but called the scenario "hypothetical" as talks are "making some progress." He said talks continue to be "productive" but that "we have not yet received the specific, tangible commitments we and the international community require." 

On Tuesday, negotiators had been trying to agree to simply a joint statement that could justify talks continuing until a final June deadline. 

Iran's deputy foreign minister, Abbas Araghchi, told reporters that if the sides make progress on the text of a joint statement, then that could be issued by the end of the day. But he suggested the statement would contain no specifics. 

A senior western official quickly pushed back, saying that nothing about a statement had been decided and that Iran's negotiating partners would not accept a document that contained no details. 

The German Foreign Ministry tweeted that "nothing is agreed," although "progress is visible." 

Araghchi named differences on sanctions relief on his country as one dispute, along with disputes on Iran's uranium enrichment-related research and development. 

"Definitely our research and development program on high-end centrifuges should continue," he told Iranian television. 

The U.S. and its negotiating partners want to crimp Iranian efforts to improve the performance of centrifuges that enrich uranium because advancing the technology could let Iran produce material that could be used to arm a nuclear weapon much more quickly than at present. 

The exchanges reflected significant gaps between the sides, and came shortly after the end of the first post-deadline meeting between U.S. Secretary of State John Kerry, his British and German counterparts and Iranian Foreign Minister Mohammed Javad Zarif in the Swiss town of Lausanne. They and their teams were continuing a marathon effort to bridge still significant gaps and hammer out a framework accord that would serve as the basis for a final agreement by the end of June. 

Eager to avoid a collapse in the discussions, the United States and others claimed late Tuesday that enough progress had been made to warrant an extension after six days of intense bartering. But the foreign ministers of China, France and Russia all departed Lausanne overnight, although the significance of their absence was not clear. 

Kerry postponed his planned Tuesday departure to stay in Lausanne, and an Iranian negotiator said his team would stay "as long as necessary" to clear the remaining hurdles. 

Officials say their intention is to produce a joint statement outlining general political commitments to resolving concerns about Iran's nuclear program in exchange for sanctions relief. In addition, they are trying to fashion other documents that would lay out in more detail the steps they must take by June 30 to meet those goals. 

The additional documents would allow the sides to make the case that the next round of talks will not simply be a continuation of negotiations that have already been twice extended since an interim agreement between Iran, the United States, Russia, China, Britain, France and Germany was concluded in November 2013. Obama and other leaders, including Iran's, have said they are not interested in a third extension. 

But if the parties agree only to a broad framework that leaves key details unresolved, Obama can expect stiff opposition at home from members of Congress who want to move forward with new, stiffer Iran sanctions. Lawmakers had agreed to hold off on such a measure through March while the parties negotiated. The White House says new sanctions would scuttle further diplomatic efforts to contain Iran's nuclear work and possibly lead Israel to act on threats to use military force to accomplish that goal. 

Israeli Prime Minister Benjamin Netanyahu continued to question the course of talks on Wednesday. 

He said Iran views Israel's destruction as non-negotiable, "but evidently giving Iran's murderous regime a clear path to the bomb is negotiable. This is unconscionable," he said. "At the same time, Iran is accelerating its campaign of terror, subjugation and conquest throughout the region, most recently in Yemen." 

Netanyahu said a better deal would "significantly roll back Iran's nuclear infrastructure" and link a lifting of restrictions on its nuclear program to "a change in Iran's behavior." 

The Associated Press contributed to this report.