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The warnings trickled in soon after an announcement began circulating last month that James A. Baker III, the former diplomat who is now a foreign policy adviser to Jeb Bush, would be a featured speaker at a conference hosted by J Street, the liberal pro-Israel advocacy organization.

It could be problematic, conservative donors and Israel hawks told Mr. Bush’s team, if Mr. Baker spoke at the event, according to three people briefed on the discussions.

But Mr. Bush’s team ultimately concluded that Mr. Baker, a former secretary of state and a longtime Bush family friend, was not someone they could pressure. And in the days since Mr. Baker’s speech — in which he criticized Prime Minister Benjamin Netanyahu of Israel for failing to work harder for Mideast peace — the criticism from Republicans has only intensified.

The perceived breach presents a new and potentially significant obstacle for Mr. Bush as he seeks to lock up prohibitive support of the Republican donor class for his presidential campaign.

Sheldon Adelson, the billionaire casino mogul and a powerful donor to Republican “super PACs,” is among those who have expressed concerns to Mr. Bush’s friends and allies, several of them said. Mr. Adelson is said to be incensed over Mr. Baker’s comments and the lack of pressure put on him by the Bush team before his address — a significant concern, given that Mr. Adelson has the resources to pour tens of millions of dollars into the Republican presidential primary.

But the flare-up could thrust Mr. Bush into conflict with some of the most hawkish voices in his party, including some leading Republican donors, and a constituency determined to demonstrate its strength in the primary.

“A few months ago, people I speak to thought Jeb Bush was the guy. That’s changed,” said Morton A. Klein, president of the Zionist Organization of America, a conservative pro-Israel organization.

Mr. Bush has responded to the criticism carefully. His spokesman issued statements criticizing J Street ahead of the speech. On Wednesday, after the speech, Mr. Bush wrote an opinion article for the National Review criticizing President Obama’s handling of nuclear talks with Iran. But he declined to disavow Mr. Baker even as he described the J Street appearance, in a television interview, as not “appropriate.”

A spokesman for Mr. Adelson did not respond to requests for comment.

Kristy Campbell, a spokeswoman for Mr. Bush, said in an email in response to questions about the lingering concerns that the likely candidate “publicly and privately has expressed that he has a great deal of respect for Secretary Baker and his accomplishments, but he thinks J Street is wrong and their actions undermine the safety and security of our close ally, Israel.”

She added that he consults with a number of foreign policy advisers and said, “Governor Bush’s support for Israel and Prime Minister Netanyahu is unwavering, and he believes it’s critically important our two nations work seamlessly to achieve peace in the region.”

The tension has created awkwardness for some longtime Bush allies who are also active in pro-Israel groups like the Republican Jewish Coalition, which is principally funded by Mr. Adelson. In interviews or e-mails, several played down the disagreements, echoing the fledgling Bush campaign’s argument that Mr. Baker is an accomplished statesman and only one of a dozen foreign policy advisers to Mr. Bush.