President Obama's freshly cut nuclear deal with Iran faces new challenges in the Senate, where lawmakers, including fellow Democrats, are intent on imposing tougher economic sanctions on Iran despite presidential warnings that such a punitive move would derail diplomatic efforts to curb Tehran's nuclear ambitions.

The United States and five other world powers meeting in Geneva last month struck a six-month accord with Iran that would ease some international economic sanctions on the Islamic republic if Tehran scales back its nuclear program. The Obama administration hailed the pact as the first critical step toward a long-term deal to end Iran's pursuit of a nuclear weapon.

Under the new deal, Iran will reduce uranium enrichment and agree to daily inspections of nuclear sites. In exchange, economic sanctions, including restrictions on the sale of Iranian oil, would be lifted and about $7 billion would pumped into the Iranian economy.

But reviews of the nuclear deal were less rosy on Capitol Hill, where the Senate's No. 3 Democrat, Chuck Schumer of New York, called the deal a "historic mistake." Lawmakers insist that the way to halt Iran's uranium enrichment activities is to get tougher with Tehran by imposing the new sanctions.

At the request of the White House, Congress put on hold any action on the sanctions while six-nation negotiations continued in Geneva. But now that Congress has seen the deal -- which allows Iran to continue enriching uranium, though at a reduced rate -- lawmakers renewed their threat to take a tougher line.

"It's very difficult to understand that at the height of our leverage, we have six countries negotiating and the world behind us, we negotiated a deal of this nature with not a single centrifuge being dismantled," Sen. Bob Corker, of Tennessee, the top Republican on the Senate Committee on Foreign Relations, told CBS. "All of them spinning in perpetuity for the next six months."

Senate Democrats who control the chamber and provided a bulwark for the president in the past are this time joining with Republicans to create new sanctions that would be imposed in six months if Iran doesn't comply with the short-term deal. Even the delayed implementation wasn't enough to satisfy the White House.

White House press secretary Jay Carney said any new sanctions would create "a march to war" for Iran. A nuclear Iran, the administration has cautioned, is a threat to the entire Middle East, particularly Israel.

Even Democrats dispute that claim on Capitol Hill, insisting new sanctions would give Tehran a greater incentive to negotiate.

"I think it's a very responsible position," Senate Foreign Relations Committee Chairman Bob Menendez, D-N.J., told CBS. "I think creating a sanctions regime that is an insurance policy and also creates leverage for us is incredibly important."

Schumer told an Orthodox Jewish group that the U.S. should continue to increase pressure on Iran "until Iran gives up not only its nuclear weapons, but all nuclear weapon capability and all enriched uranium."

Senate Majority Leader Harry Reid, D-Nev., who decides which issues the chamber takes up, said in a recent interview that he intends to hold a vote on the sanctions despite the president's warnings.

"I still feel the same way today," Reid told NPR. "I said when we come back we will take a look at this to see if we need stronger sanctions."

The White House is worried. The Republican House has already expressed support for new sanctions and If the Democratic Senate approves them there would be nothing stopping the bill from reaching the president's desk.

The administration has dispatched former ambassadors and others to Capitol Hill to help convince Congress that there's no need for sanctions. The pro-Obama group Americans United for Change, meanwhile, is spreading the word that its polling shows the vast majority of voters support Obama's deal. That poll also showed that voters don't necessarily favor new sanctions if they would derail diplomatic efforts.

"The clear majority of voters do not want Congress to impose more sanctions at this point if doing so might jeopardize the agreement and the on-going negotiations," said Hart Research Associates President Geoffrey Garin, whose firm conducted the survey.