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None of that means Jeb Bush will run. He has said he will decide by the end of the year, and could simply be keeping the possibility open to enhance his influence on the political stage. To some who have spoken with him in recent months, he has not exhibited the same fire that his father and brother did at this stage in the process.

Advisers to Bush said he has not authorized anyone to line up money or people to work for him. Some of the positions he has taken on immigration, taxes and education are at odds with the prevailing orthodoxy of his party. He knows he would have to find a way to distance himself from some of the unpopular decisions of his father, and especially of his brother.

And he has said publicly he does not want to run if it means getting caught in the “vortex of a mud fight,” acutely aware of the perils of bringing his family into the harsh light of modern politics. Columba was once stopped by customs agents for not declaring the full value of $19,000 in clothing and jewelry she bought in Paris, and their daughter Noelle was arrested for prescription drug fraud a dozen years ago.

“He has certainly not given anyone I’m aware of the ability to have conversations with potential donors or staff to keep his powder dry,” said Sally Bradshaw, a longtime adviser. “That doesn’t mean people don’t call us and say we want Jeb to run. But he has not given a green light to that.”

Having said that, Bush has been active on the campaign trail, effectively building up chits. He has appeared at more than 35 campaign events for such figures as Govs. Nikki R. Haley of South Carolina, Susana Martinez of New Mexico, Mary Fallin of Oklahoma and Rick Snyder of Michigan and Senate candidates like Joni Ernst in Iowa, Tom Cotton in Arkansas and Cory Gardner in Colorado.