The Obama team, on the other hand, sees the six-month interim accord as the first step toward a final deal that ends the nuclear threat and might moderate Tehran's bad behavior in the region.
Both opponents and proponents of the deal could benefit from a reality check.
For starters, despite claims to the contrary, passage of the Kirk-Menendez bill would kill the talks. True, it was the harsh bite of economic sanctions - which halved Iran's oil exports - that brought Iran to the table. But the provisions in this bill, known as the Nuclear Weapon Free Iran Act of 2013, rule out any chance of a final deal.
The legislation would impose new sanctions to slash Iran's oil exports to nearly zero - unless Iran completely dismantles its nuclear infrastructure, including any uranium enrichment facilities. The Iranians have made very clear that they will never totally give up their capacity to enrich, which they are entitled to if - a big if - they convince the world their program is peaceful.
There are many provisos that concerned senators could call for in a final agreement in order to delimit the Iranian program, but ruling out any low-level enrichment is unrealistic. So is the demand that Obama certify that this is the goal the United States seeks.
Equally disturbing is a provision in the bill that requires the United States to give military backing to Israel if it decides to take military action against Iran's nuclear program. While U.S. support for Israel's security is - and should be - strong, no president can make a blanket commitment to wage another Mideast war in undefined circumstances at another country's discretion.
The White House angered senatorial supporters of the bill by daring them to admit they want a war with Iran. Sen. Robert Menendez (D., N.J.) calls his bill "a diplomatic insurance policy" that will force Iran to close down its nuclear program. Yet demanding a perfect deal or none at all - the position of Israeli leader Benjamin Netanyahu, which has strong support in Congress - does doom diplomacy. This makes it fair to ask the 59 senators if they are ready for another Mideast war.
Indeed, the whole Iran debate would be healthier if it were possible to openly discuss what Americans are willing to do if there is no Iran deal.
"Those are issues nobody wants to deal with," says Kenneth Pollack, author of Unthinkable: Iran, the Bomb, and American Strategy, because all of the options are bad.
"The real choice is between going to war and containing Iran," Pollack said this week at the Foreign Policy Research Institute in Philadelphia. (Pollack would choose containment, an option too rarely discussed in Washington.)
"I am convinced this administration has no desire to go to war with Iran, which is why they are so desirous of a deal, to a degree that sometimes worries me," Pollack adds.
Indeed, here's the rub for Obama: He is correct to want to avoid a war with Iran, which would not destroy its nuclear program but might actually accelerate it - and would lead to untold negative consequences in an unstable region. But if he wants to win congressional support for a diplomatic deal - the best of the bad options - he must convince Congress that he won't give away the store.
Unfortunately, the president's overall Mideast policy does not create confidence. His failure to stand by his own red lines on Syria, and to bolster non-Islamist Syrian rebels, has convinced Arab, Israeli, and Iranian leaders that he is weak.
To win over Congress - where the vote on the Kirk-Menendez bill is on hold for now - Obama must do more than defend diplomacy. He must convince legislators that the White House is tough enough to hold out for the best possible deal, and to push back against dangerous Iranian behavior in Syria and Iraq.
The president must also make clear to Americans and to Congress that the options are all risky. With Iran, holding out for the perfect will eliminate any chance for a reasonable deal.