The United States is prepared to allow Iran to recoup up to $10 billion in revenues lost to sanctions, according to a U.S. government estimate of sanctions relief proposed this weekend at Geneva.

Three sources briefed by the Obama administration this week on the talks between Iran, the United States and five other great powers, say that U.S. estimates on the value of special exemptions to allow Iran to sell and ship some of its oil and other exports would result in no more than $10 billion worth of sanctions relief.

Colin Kahl, a former senior Pentagon official in Obama’s first term and an expert on U.S. policy to Iran, said in testimony before Congress Wednesday that the package being proposed to Iran was worth no more than $6 to $7 billion in sanctions relief.

For Iran, this relatively modest sanctions relief—compared to the losses it has suffered as a result of its isolation from the world economy—matters. A recent report from the Foundation for the Defense of Democracies and Roubini Global Economics estimates Iran’s government has access to only $20 billion in overseas foreign reserves that it can spend with no restrictions.

The freeze on Iranian revenue is the result of a sanctions regime that has blacklisted the country’s economy from the global financial sector. As a result, Iran has had trouble finding the insurers, banks and shipping companies willing to risk trading Iranian oil.

Under the proposal offered in Geneva, Iran would be allowed to sell $3.5 billion worth of its oil in the next six months and a few billion more in sales for its gold, petrochemical and automotive sector, according to briefings from the Obama administration described to The Daily Beast.

The Israelis have said the value of the sanctions relief is more than the Obama administration has been claiming. On Wednesday, Israel’s Strategic Affairs Minister Yuval Steinitz told reporters that the sanctions relief package being offered to Iran would provide Tehran with $15 to $20 billion of direct relief and that proposed enforcement easing would make the total value of the deal around $40 billion for the Iranians.

State Department spokeswoman Jen Psaki Wednesday disputed those figures, saying: “Without going into specifics about what we're considering, that number, I can assure you, is inaccurate, exaggerated, and not based in reality.”

Nonetheless, the Israelis and other critics of the proposed sanctions relief say there is a risk that any loosening of pressure on Iran before it begins dismantling its nuclear program could encourage countries, banks, and other institutions to skirt existing sanctions and offer Iran's isolated and pressured economy a life line.

“Business with Iran is driven by greed and fear,” said Mark Dubowitz, the executive director of the Foundation for Defense of Democracies, a think tank that has supported escalating sanctions on Iran. “In an environment of escalating sanctions where the U.S. surrounds Iran with an economic minefield, fear overrides greed. When sanctions are being de-escalated, as they are today at the request of the administration, greed will override fear.”

Many members of Congress also take the view that no financial pressure on Iran should be relieved until Iran begins to dismantle its centrifuges at Natanz and Qom, or at the very least, until it stops enriching uranium. Until then, senators from both parties have said they support a new round of sanctions aimed at tightening the squeeze on Iran even during negotiations.

The Obama administration has made the case that it needs to offer limited sanctions relief to Iran in exchange for more rigorous inspections and more transparency from the country regarding its nuclear program. Some sources briefed on the negotiations say Iran is prepared to cap the total amount of nuclear fuel it will store at any one time in the six-month negotiation period.

On Wednesday, a showdown between Congress and the administration took place at the Capital Building. In a closed session, Secretary of State John Kerry, Undersecretary of State for Political Affairs Wendy Sherman, and Undersecretary of Treasury David Cohen spoke to members of the Senate Banking Committee and Senate leadership from both parties.

Sen. Bob Corker (R-TN), who is also the ranking Republican on the Senate Foreign Relations Committee, emerged from the briefing flabbergasted that the officials refused to tell senators any details of the pending agreement. “It was an emotional appeal and I was very disappointed in the presentation. It lacked content,” Corker said. “If I were trying to convince somebody of something, I would lay out details. I am stunned that in a classified setting… there would be such a lack of specificity.”

Sen. Mark Kirk (R-IL), who is preparing his own legislation to tighten sanctions on Iran, got into several heated discussions with the officials inside the classified briefing, he said. Kirk said the Israeli government briefed him on the proposed agreement Wednesday morning and told him the Iranian concessions would only amount to a 24-day delay in their progress towards nuclear capability—and in exchange, Tehran would receive billions of dollars worth of sanctions relief.

“The briefing was fairly anti-Israeli. I was supposed to disbelieve everything the Israelis just told me. I don’t. I think the Israelis probably have a pretty good intelligence service,” Kirk said. “The administration very disappointingly said ‘Discount what the Israelis say.’ I think that was wrong as a policy matter.”

Kirk said he would use every legislative avenue available, including the upcoming debate over the National Defense Authorization Act (NDAA), to try to secure a vote on a new sanctions package. He reminded the officials that the last sanctions package he sponsored with Senate Foreign Relations Committee Chairman Robert Menendez (D-NJ) passed the senate by a vote of 100-0.

Several GOP Senators compared the Obama administration’s strategy towards Iran to the Clinton administration’s strategy towards North Korea, in which Sherman herself was involved. A 1994 framework agreement with Pyongyang was hailed at the time but was later scuttled due to North Korean cheating. North Korea subsequently tested a nuclear device on three separate occasions.

“After Wendy led the effort to give North Korea nuclear reactors and food, her record on North Korea is a total failure and an embarrassment to her service,” said Kirk. “Today is the day when I witnessed a future of nuclear war in the Middle East some day that will be part of our children’s heritage. This admin, like Neville Chamberlain, is yielding a large and bloody conflict in the Middle East involving Iranian nuclear weapons.”

Sen. Lindsey Graham (R-SC) also said that the North Korean example looms large as senators consider whether to pause their sanctions push against Iran. He also said senators don’t trust the administration to negotiate a good deal.

“There’s a real belief among members of Congress on both sides of the aisle that the administration wants a deal too much,” Graham said. “You should not begin to put any capital into the Iranian economy until they begin to dismantle the centrifuges.”

State Department Spokeswoman Jen Psaki, previewing Kerry’s pitch before his Capitol Hill meetings, said that Kerry would tell senators that more sanctions now could ruin the negotiations and start both sides on the path to war.

“We put crippling sanctions in, not just to bring Iran to the table, but to give us the strongest possible hand at the negotiating table with the greatest amount of leverage and international support. And the sanctions now have worked,” she said. “This is a vote for or against diplomacy… I think the consequences of not moving forward with a diplomatic path is potentially aggression, potentially conflict, potentially war.”