The talks now look set to continue at least until Friday, past the July 9 date by which Congress was to receive a copy of the agreement for its review. According to legislation, Congress would have had 30 days to examine the deal and pass a resolution of disapproval to block its implementation, but with talks passing that deadline, they will have 60 days.
Multiple Republican aides in both the House and Senate said that a longer review period would give critics more time to poke holes in a deal and whip up opposition. Already, Republican leaders have warned U.S. officials not to buckle to Iran's last-minute demands.
One senior House GOP leadership aide predicted that the administration could also face more resistance from fellow Democrats as members have more time to sift through the deal's details.
"If the White House is as successful with their Democratic members as they were on trade, they are going to have a real tough time," the GOP aide said, referring to the significant percentage of President Barack Obama's party that opposed him on a recent bill to fast-track a major pan-Pacific pact.
Already one significant Democratic voice is sounding concerns about the deal that are in line with Republicans.
Referring to the longer review period for the deal, House Democratic Whip Steny Hoyer told reporters Tuesday, "This is a very serious agreement -- I think that's not bad."
And the Maryland representative expressed reservations about continuing talks with Iran.
"My concern has been that there will be a rope-a-dope sort of performance by Iran and they'll just string out these negotiations," explained Hoyer. "It appears the Iranians are unwilling to meet the requirements that are necessary in order for there to be an agreement."
At the same time, Hoyer agreed with Senate Foreign Relations Chairman Bob Corker, a Tennessee Republican, who has said recently that negotiators should continue discussions if needed past July 9 because "time limits ought not to be the issue here."
Corker, who will lead the Senate in examining a deal through a series of hearings and briefings, spoke for many critics Tuesday when he told MSNBC he is "very concerned about the trend" and "direction of these negotiations." He described himself as "fairly despondent" over it.
House Foreign Affairs Committee Chairman Ed Royce, a California Republican, released a statement Tuesday saying "there is no push" from Congress to wrap up the talks this week. He added, "If the administration negotiates a sound agreement, it should be able to withstand congressional scrutiny for 30, 60, or even 90 or 120 days."
Democrats on the Hill beyond Hoyer seem resigned to an extended review for the Iran nuclear deal.
"I think the administration knows this is a tough issue no matter what -- a 30 or 60 day review. That's the deal that was made and we'll just have to work with them," New York Democratic Rep. Joe Crowley told CNN.
As for critics using the extended time to build opposition to a deal, Crowley shrugged and said, "as we say in New York - it is what it is."
The law passed in May providing for congressional review of a deal with Iran actually stacks the decks against Capitol Hill, where most in the Republican majorities of both chambers are highly skeptical of the President's ability to cut a tough and lasting deal with Iran. That's because the President would likely veto any resolution of disapproval and require opponents to muster a supermajority of 67 votes in the 100-seat Senate and 290 votes in the 435-seat House to override his veto.
That presents a daunting task, but not an impossible one, especially if the deal appears weak. In the Senate, 14 Democrats have raised doubts about the deal, meaning a veto override vote could be razor-thin if those 14 don't like the deal.
Obama administration officials have repeatedly stressed that they'll only accept a good deal from Iran and think the public will back the result when they see what it contains.
They have also said that there is no guarantee a deal will result, as they are still seeking key concessions from Iran. In particular, they are insisting that they will not waver on the key point of putting in place a rigorous inspections and verification mechanism that would allow international monitors to review any suspicious facility throughout Iran.
Obama plans to talk to Senate Democrats about the Iran deal at a meeting with them later Tuesday.
And top leaders on Capitol Hill are getting regular briefings on the status of the negotiations, according to two Republican congressional sources.
Next week, the House Foreign Affairs Committee will hold the first in a series of hearings it is planning on any Iran deal. These forums will give opponents another platform to pick apart an agreement. Kerry is expected to be invited to testify.
Heavy lobbying on the issue is also expected from interests groups like AIPAC, the American Israel Public Affairs Committee, which is influential with lawmakers from both parties and is very anxious that a nuclear Iran threatens Israel.
The 2016 presidential campaign, including the five senators currently running for the White House, could also supercharge the atmosphere when the debate takes place.
One Republican candidate, Sen. Ted Cruz of Texas, issued a statement Monday calling the Iran negotiations a "disaster" and urged all the other presidential candidates -- including Democrats -- to join him in "demanding that Secretary (John) Kerry stop negotiating with this hostile and violent enemy of America and immediately leave Vienna."
Another GOP senator, Marco Rubio of Florida, released a statement after the deadline was moved again on Tuesday, saying, "The Obama administration's decision to extend nuclear talks with Iran for the second time in one week is just another sign that it is time for President Obama to walk away from the table."
Members from both sides say they want to carefully review the details of any deal, but how Iran interprets those details will also be critical. In April, when the administration rolled out the initial framework of a nuclear agreement, top Iranian officials quickly contradicted many of the details. Those mixed messages, particularly about how sanctions could be lifted, only contributed to the reservations many on Capitol Hill had about how lasting an agreement with Iranian leaders could be. If that process repeats itself, it could torpedo any effort by the administration to get Congress on board.
State Department spokeswoman Marie Harf said Tuesday morning in a statement that U.S. officials have "made substantial progress in every area" and will continue negotiating with their Iranian counterparts through Friday. This is the second time negotiators have extended the deadline, which was originally set for June 30.
"This work is highly technical and high stakes for all of the countries involved. We're frankly more concerned about the quality of the deal than we are about the clock, though we also know that difficult decisions won't get any easier with time -- that is why we are continuing to negotiate," Harf said.
A senior administration official reiterated Tuesday afternoon that while the sides have never been closer to a deal, they're still not where they need to be and whether a deal is reached could go either way.
However, the U.S. believes it's possible to reach an agreement, and places a high priority on getting it done.
"All of us feel it would be really, more than unfortunate, it would be quite a tragedy if we've come this far -- we have really made a significant and substantial amount of progress, quite extraordinary -- it would be very, very unfortunate if we could not get it done," the official said.