WASHINGTON — Jeb Bush has long resisted pressure from supporters to run for president. Now the former Florida governor is signaling that he’s at least open to the idea, a shift that comes as he promotes a new book and Republicans struggle to rebound after President Barack Obama’s re-election.

“I’m not saying yes. I’m just not saying no,” Bush told NBC News earlier this week, one of a series of such comments he’s made as he talks about the book “Immigration Wars” in television interviews and forums.

Comments like those from Bush, 60, are in sharp contrast to past refusals to even entertain the idea of following in the footsteps of his older brother, former President George W. Bush, and their father, former President George H.W. Bush.

Less than three years before the first Republican presidential primaries, Bush’s words offer a window into his evolving thinking on a future run. Republicans and former advisers said that, if nothing else, he’s made clear to political operatives and donors that they shouldn’t count him out for 2016.

“He’s sent a very strong signal this week that he, for the first time, is going to seriously, seriously consider running,” said Cory Tilley, a former Bush aide in Florida. “It’s the signal that a lot of people have been waiting to hear.”

The scion to the Bush political dynasty left the Florida governor’s office in 2007 but since then has remained a major figure in the GOP, mainly through his efforts to influence education and immigration policy. His book is his latest step on that front; in it, he urges Congress to revamp a broken immigration system that he says is holding back the nation’s future and economic growth.

He caused a stir and irked some Republicans by writing that he did not support a pathway to citizenship for undocumented immigrants. Bush had expressed support for a pathway in the past, and later said he was open to a pathway to citizenship as long as it did not encourage illegal immigration.

That shift aside and even without the famous last name, Bush would have strong presidential candidate credentials. In the important swing-voting state of Florida, Bush racked up strong job performance ratings while revamping the state’s educational system, reorganizing government, cutting taxes and managing the state through several hurricanes.

His wife, Columba, is Mexican-American and Bush is fluent in Spanish. He won over a diverse electorate of Hispanics in Florida. That personal and political history could help him to connect with Latinos, significantly more of whom voted for Obama than Republican Mitt Romney last fall.

Even so, Bush would have vulnerabilities as a candidate — perhaps the biggest being his last name.

George W. Bush was unpopular when he left office in 2009. He continues to have approval ratings below 50 percent, and exit polls conducted last November found more voters blamed the former president for the nation’s economic woes than Obama.

Jeb Bush has expressed pride for his brother’s time in the White House and said perceptions of his brother would not factor into his own future.

Until recently, he has consistently said he wasn’t interested in pursuing national office. In a CBS News interview last year, he speculated that 2012 “was probably my time” to run for president, all but ruling out a future bid.

He’s now consistently saying a version of what he told NBC: “Every election is a little different. And so I don’t know. I don’t know what the rhythm and pace of 2014 looks like, much less 2016. But I think you have to understand, though, that we need to be the governing party.”

“For him not to rule this out immediately shows that there’s more going on,” said Slater Bayliss, a lobbyist and former Bush aide based in Tallahassee, Fla.

Much has happened since Bush departed the governor’s office in Tallahassee in 2007. From the sidelines, he watched the Great Recession, the rise of both Obama and the tea party, and ongoing budget battles.

Despite his TV appearances, Bush’s book tour does not exactly resemble the itinerary of a future presidential candidate — he has no immediate plans to go to Iowa and New Hampshire, the first states to hold nominating elections. He started the week in New York and planned to travel to Washington before weather forced event cancellations. Bush was scheduled to appear at the Ronald Reagan Presidential Library in Simi Valley, Calif., on Friday, in the northern Kentucky suburbs of Cincinnati on March 14 and at a private event in Phoenix on March 18.

On March 15, Bush will keynote the Reagan dinner at the Conservative Political Action Conference, a plum speaking role at the annual gathering of prominent conservatives. And next month, George W. Bush will dedicate his presidential library in Dallas, bringing more attention to the Bush legacy.

Republicans say the younger Bush has plenty of time to consider his options.

“I don’t think he has to have a master plan at this point. He can do well by doing good,” said Sara Taylor Fagen, who was a political director for President George W. Bush. “If he chose to run it would ultimately accrue to him and his brand and his abilities.”

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