Speaking at a news conference during an annual congressional trip to Israel, McCarthy said there's "very [much] a possibility" that there could be enough votes for the override, which the administration has said would sink the deal.
He also said that the White House's relying on the support of just over one-third of Congress -- the number needed to sustain a veto -- for a major diplomatic agreement is too little.
McCarthy noted that Obama did not designate the deal a treaty, which would have required a much higher level of Senate support to be ratified. "Now he's playing to hold one-third. If you try to make an agreement where only the minority of your country is going to support [it], that majority is going to have a voice one day."
He predicted that the deal would "play very large" in the presidential race.
Nearly all the Republicans are expected to vote against the deal, so President Barack Obama's chances for sustaining a veto hinge on keeping 13 Senate and 44 House Democrats from rejecting the agreement.
So far the White House has been confident it can retain the necessary Democratic support.
The deal picked up more key backers on Thursday. That morning, Al Franken became another Senate Democrat, and Jewish lawmaker, to voice his support for the deal. In a CNN op-ed
, the Minnesota Democrat said he weighed the decision heavily, discussing the issue with a number of representatives from both sides.
"It isn't a perfect agreement," Franken wrote. "But it is a strong one. This agreement is, in my opinion, the most effective, realistic way to prevent Iran from getting a nuclear weapon anytime in the next 15 years."
Sen. Jon Tester also said he would support the deal.
"After reading the agreement, consulting with experts and listening to Montanans, it's clear this deal is the only option right now to stop Iran from developing a nuclear weapon," Tester said in a statement.
The Montana senator is not only a red-state Democrat, but also the chairman of the Democratic Senatorial Campaign Committee, signaling that he felt safe that his support of the deal would not be a political vulnerability.
Late Wednesday, Chicago Mayor Rahm Emanuel announced he is supportive of the deal. Obama's first chief of staff is an influential Jewish politician nationally.
"I would say to you this agreement is a good agreement and it is far superior to either sustained bombing that would never actually get you what you have today or sanctions that would exist on paper but with no international support," Emanuel told The Huffington Post
Franken and Tester became two of 19 Democratic and left-leaning independent senators who have said they will back the deal.
If trends continue, the White House could pick up enough Democrats to block consideration of the disapproval in the Senate altogether, by not giving Republicans 60 votes to move the bill forward.
Obama deployed one of the administration's top deal negotiators on Thursday to continue to build support for the deal. Energy Secretary Ernest Moniz, a nuclear physicist, participated in a live-streamed conversation with the Jewish Federation of North America to answer questions about the Iran deal and explain the White House's thinking on it.
The Jewish community and pro-Israel lobby in the U.S. has been some of the biggest opponents to the deal.
"To be honest, if you go back to the discussions among the experts prior to the Lausanne framework in early April, you will see that every dimension of this agreement beats the expectations," Moniz said. "This is already the famous 'better deal.' We have it."
He answered specific, technical questions on the mechanisms of enforcement in the deal, and said one of the important factors is not squandering the international unity, including with Russia and China, that has brought the deal about.
"Honestly, I have not heard a credible plan B. I just haven't heard it. And I do know, as we said earlier, that if we are the ones who unilaterally undermine this agreement, it's not going to be a very good day after," Moniz said. "If that leads, as I believe it will, to a fraying of the economic sanctions regime ... then we could end up with the worst of all worlds, with an unconstrained nuclear program, fraying sanctions and international disunity that Iran will be able to capitalize on."
So far, the GOP only has one solid Iran detractor in the Senate in New York Democrat Chuck Schumer, but Senate Majority Leader Harry Reid said Wednesday evening that he is still undecided. He told the Las Vegas Review-Journal
that he will make his decision when he's "ready," but first wants to talk through the debate with several friends he feels he "owes" it to.
"I just have to work through some of my personal issues, because when it all boils down to it, it's a question of conviction. It's not a political calculus for me anymore," Reid said. "It's an extremely difficult issue. ... I'm going to try to talk everyone I can."
He also noted that Schumer's opposition was not a surprise to him.
"I've known for a long time how he was going to vote," Reid told the paper. "He didn't tell me, but I knew, he didn't need to tell me. We've been around each other so much we pretty well understand each other."
He noted he'd continue talking to Schumer, and that his No. 2 Democrat, Illinois Sen. Dick Durbin, was leading the charge for the White House to whip up support among Dems.
"Durbin is the key guy out front on this one. He's the one doing the work," Reid said.
Reid stressed that he is meeting with a range of groups, saying, "there are two groups of Jews -- one are the religious Jews and they have strong feelings. But also the non-religious Jews, who are extremely concerned about Israel."
The Baltimore Sun editorial board on Wednesday wrote in favor
of the deal -- which could reach two more key undecided Democrats from Maryland.
Sen. Ben Cardin, ranking member of the Senate Foreign Relations Committee, indicated to The Washington Post
that he would wait until after Labor Day to declare a position. And Sen. Barbara Mikulski has not yet indicated how she will vote.
On the other side of the Hill, Obama lost a Democrat on Thursday when Florida Rep. Alcee Hastings announced he would vote against the deal. In a statement, he detailed a number of concerns with the deal, including relieving sanctions on the Iranian government.
"We must maintain a strong sanctions regime — to do otherwise is to give up our leverage," Hastings said. "Sanctions are what brought Iran to the table, and they depend on large-scale international cooperation and compliance."
Hastings makes 11 House Democrats who say they'll vote against the deal, but Obama still seems to have strong support among 146 voting Democratic lawmakers who signed onto a letter in the spring supporting negotiations.
Two Democrats in the House came out for the deal Thursday, and current and former Democrats on the House Intelligence Committee wrote a letter to their colleagues urging them to use committee resources to brush up on the deal.
"Our work on the Intelligence Committee and the insights it has given us into Iran's nuclear program -- past and present -- as well as the confidence it gives us that this agreement cuts off Iran's access to the bomb, have been significant drivers behind our decision to support the deal," the members wrote
. "We hope you will take advantage of the Intelligence Community's assessment as you make your decision."
Connecticut Rep. Jim Himes, who also signed the letter, and Massachusetts Rep. Katherine Clark both put out statements of support for the deal Thursday.