Washington (CNN) A bill that would give the Senate sign-off on an international agreement with Iran over its nuclear program will be on the Senate floor next week, despite objections from Democrats who want to wait for an agreement to be reached with Iran before passing the legislation.

"We think the timing is important," Senate Majority Leader Mitch McConnell told reporters when he announced he would fast-track the bill. "We think it will help the administration from entering into a bad deal but if they do it, it will provide an opportunity for Congress to weigh in."

The bill, which would give Congress an up or down vote on any agreement, was introduced last week by Sen. Bob Corker, the Republican chairman of the Foreign Relations Committee, and Sen. Robert Menendez, the committee's top Democrat.

But Democrats worry quick action on the bill could amp up pressure on the talks and possibly disrupt them. The negotiations, which have been going on for months, face a critical March 24 deadline.

Republicans, and some Democrats, are concerned President Barack Obama will not get a 'good deal' with Iran via negotiations and hope to have greater input.

But Menendez said he was "outraged" McConnell decided to bypass committee action on the bill and accused the majority leader of playing politics with the issue.

"I can't imagine why the majority leader, would seek to short circuit the process unless the goals are political rather than substantive," Menendez said.

Senate Democratic Leader Harry Reid weighed in as well.

"Instead of retreating to our corners and preparing for a partisan fight, everyone should take a deep breath and ask themselves: are they moving forward in the manner that will best facilitate the broad bipartisan support that has faced down Israel's enemies and protected Israel's people for decades? Or are they simply seeking to score cheap political points?" he asked.

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On another sensitive issue related to the talks, McConnell said he was open to the legislation being amended with new economic sanctions against Iran. The White House had pressed Congress to set aside new sanctions for now fearing it could cause the Iranians to leave the negotiations.

"Arguments have been made by some of our friends on the other side and the administration that the choice was between this deal and war," McConnell said, indicating that theory is incorrect. "The choice is between this deal and tougher sanctions."

Multiple lawmakers told CNN that Netanyahu's hard hitting-speech warning about the impact of a deal with Iran was effective and gave new momentum to members who want to approve new sanctions.

Corker explained how the bill would allow Congress to closely examine a deal reached with the Iranians.

"For 60 days it would lay before Congress. We would have the opportunity for hearings, and to have classified briefings, and to understand what the President has agreed to," he said. "During that period of time Congress can either approve, disapprove or take no action at all."

Corker said if Congress signed off on the deal, the administration would have to make regular reports to Congress about whether the agreement was holding.

"Every 90 days, the President has to certify to us they're not developing a nuclear weapon, that there is no covert activity occurring, and there is not terrorism being conducted against the U.S. or its allies," Corker said.

Bernadette Meehan, spokeswoman for the National Security Council, said Tuesday night Obama would veto the Corker-Menendez measure if it landed on his desk.

"The President has been clear that now is not the time for Congress to pass additional legislation on Iran," she said in a statement. "If this bill is sent to the President, he will veto it. We are in the final weeks of an international negotiation. We should give our negotiators the best chance of success, rather than complicating their efforts."

Asked whether Senate Democrats would agree to take up the proposal, Reid said he'd prefer to wait until after the March deadline to take up the bill.

"Why don't we wait until we see what happens. We have just three weeks left, as I understand, and we should know whether we're going to have a deal with the Iranians," Reid said. "I personally am going to wait and see what happens, whether we have a deal and then look at all the legislation at that time."