House Majority Leader Kevin McCarthy, R-Calif., said enough opposition is mounting to the Iran nuclear agreement among lawmakers that they could override a presidential veto and kill the deal.

"I don't believe a veto-proof majority is out of reach," McCarthy told reporters on Tuesday.

Republicans are angry that the Obama administration allowed a United Nations vote on the deal to proceed before Congress had an opportunity to review the deal. They didn't like the deal to being with either, and say it falls far short of curbing Iran's nuclear ambitions.

A 60-day congressional review clock began on Monday, and is expected to end in September with a GOP attempt to pass a resolution disapproving of the agreement.

McCarthy said he believes the White House is looking to secure "a little more than a third of Democrats, to uphold the veto," that Obama would issue if Republicans pass the resolution of disapproval.

Many in the GOP oppose the terms of the deal because they believe it will not stop Iran from obtaining a nuclear weapon and allows the Russians to sell ballistic missiles to Iran in less than a decade. The deal also allows Iran up to 24 days notice ahead of an inspection.

"The more people learn about it, the stronger the vote to disapprove will be on both sides," McCarthy said.

McCarthy said the U.N. vote ahead of Congress, "will backfire on him," by alienating lawmakers.