Jay Carney, the White House press secretary, said the president had also dispelled reports that a deal would give Iran sanctions relief worth $40 billion to $50 billion — a range he said was inaccurate. He did not provide an alternative figure, though a person in the meeting said the administration had estimated the package on the table was worth $5 billion to $10 billion.

In the meeting, Secretary of State John Kerry argued that lifting these sanctions would not materially improve Iran’s economic plight. Other officials noted that with sweeping oil sanctions still in place, Iran would lose $30 billion in oil revenues during the six months of the deal.

Yet critics in the Senate said there was a psychological dimension: The Iranian leadership will react differently if it thinks sanctions can get worse as opposed to believing they will get better.

In the letter to Mr. Obama, senators expressed concern that the deal would allow Iran to continue enriching uranium to 3.5 percent and would permit some construction to continue at the heavy-water reactor at Arak, which could eventually produce plutonium — a fuel for nuclear bombs. And while a deal would limit the number of centrifuges Iran would be allowed, it would not require Iran to dismantle existing machines.

Other critics objected that a deal would implicitly recognize Iran’s right to enrich uranium. The administration has repeatedly rejected Iran’s claim that it should have that right, but experts on Iran said they expected an interim deal to finesse the point.

“They have forfeited the right to enrich by their cheating and their lying and their prevarication for the last 20 years,” said Senator John McCain, Republican of Arizona, who also took part in the meeting. “If they want to have a nuclear power plant, we’ll build one for them.”

Despite his skepticism, Mr. McCain said he believed the president deserved some leeway to negotiate a deal. But his account of the meeting underscored how much work Mr. Obama would have to do to persuade lawmakers to support any comprehensive deal with Iran.