A White House spokesman warned that if a deal with Tehran was not agreed, Iran would continue enriching uranium.
Envoys from the P5+1 group of nations will begin a new round of negotiations with Iran in Geneva on Wednesday.
Iran’s Foreign Minister Javid Zarif said he believed issues could be resolved.
In a message on the video-sharing site YouTube, Javid Zarif said: “We expect and demand respect for our dignity. For us Iranians, nuclear energy is not about joining a club or threatening others. Nuclear energy is about a leap, a jump toward deciding our own destiny rather than allowing others to decide for us.”
Barack Obama held two hours of talks with senators at the White House on Tuesday, along with Secretary of State John Kerry and National Security Adviser Susan Rice.
In recent days some legislators have expressed concern that the White House is moving too fast and should take a harder line with Tehran.
“We have the opportunity to halt the progress of the Iranian programme and roll it back in key respects, while testing whether a comprehensive resolution can be achieved,” the White House said in a statement.
It said that if there was not an initial agreement, Iran would grow its stockpiles of enriched uranium, install new centrifuges and develop a plutonium reactor in the city of Arak.
Press secretary Jay Carney said President Obama had told the senators new sanctions would be most effective as a consequence if Iran refused to accept the deal now on the table or agreed and then failed to comply.
The president also rejected reports that Iran would receive at least $40 billion in sanctions relief.
Since 2006 the UN Security Council has imposed a series of sanctions on entities and people involved in Iran’s nuclear programme.
Separate US and EU sanctions have targeted Iran’s energy and banking sectors, crippling its oil-based economy.
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