Story highlights On Monday, Obama picked up another Democratic supporter when Sen. Brian Schatz came out in support of the deal.

"This was one of the most difficult decisions that I had to make," Sen. Chuck Schumer said.

House Minority Whip Steny Hoyer said the meetings in Israel did not allay any of his concerns with the deal.

(CNN) While President Barack Obama is in Martha's Vineyard, 22 House Democrats are in Israel being lobbied by Prime Minister Benjamin Netanyahu to oppose the Iran deal.

House Democratic Whip Steny Hoyer, speaking in Israel with CNN on Monday, said he still hasn't made up his mind on the deal -- and neither have the 21 other House Democrats on the trip -- but that he believes the President could have negotiated a better deal and conversations with Israeli Prime Minister Benjamin Netanyahu reinforced concerns he has.

"I intend to go back and spend a week with my family, but after that to give this very careful consideration, because I think it's one of the more important decisions that I will be asked to make as a member of Congress," Hoyer said.

Despite the undecided Democrats on the trip and the high-profile opposition of the Senate's No. 3 Democrat, Chuck Schumer, announced last week, the President can still probably breathe easy on his vacation when it comes to the votes needed to on his legacy-sealing agreement curbing Tehran's nuclear program.

If all House Republicans voted to override the veto, they'd still need to convince 44 Democrats to join the effort to succeed. As of Monday, nine have officially said they would vote no, and 146 voting House Democrats out of the 188-member caucus signed a letter in May supporting the Iran negotiations before a deal was reached. None of those signatories have yet come out against the deal. In the Senate, a united GOP would need six Democrats to clear a procedural hurdle and 13 to override a veto, and only Schumer has publicly said he would oppose the deal.

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