Washington (CNN) -- Jeb Bush has been doing something he's never really done before: talking publicly about running for president.
As he does the television interview circuit this week around the release of a new book, "Immigration Wars: Forging an American Solution," the former Florida governor and son and brother of former presidents is openly discussing his thinking on a run for the White House in 2016.
Bush told CNN on Tuesday he wouldn't make a decision in the near future. Asked if he'll make a decision in 2014, Bush said he didn't know and added that "the only thing I've decided is I'm not going to think about it for 2013. It's just too far out for me personally."
Bush passed on running for the Republican presidential nomination in 2008 and 2012. Instead, he's filled the role of a party elder statesman since leaving office in January 2007 after two terms as governor.
Hanging over Bush is what can be described as Bush fatigue -- the idea that a Jeb Bush bid for the White House would carry his family's political baggage.
His father, George H.W. Bush, served one term before losing his 1992 re-election campaign against then-Arkansas Gov. Bill Clinton. The elder Bush angered many conservatives by breaking his "no new taxes" pledge.
Brother George W. Bush served two terms but left office in January 2009 as a very unpopular president, even among Republicans, who were angered by his support of federal spending increases and his 2008 bailout of Wall Street during the financial crisis.
That lingering feeling was a factor behind Jeb Bush's decision not to run in the past election cycle, even though some Republicans urged him to consider a bid, said CNN chief political analyst Gloria Borger.
"One of the reasons that I think Jeb Bush decided not to run this last time was that he thought there was still Bush fatigue in this country," Borger said. "So the question is, if you skip ahead, four more years, will there still be Bush fatigue? We just don't know."
And if Bush does run, his family ties will put him in uncharted territory, said CNN polling director Keating Holland.
"There have been plenty of presidential candidates whose fathers also ran for president, and a few whose brothers have been candidates. But if Jeb Bush throws his hat in the ring, he will be the first candidate in history who fits into both categories," Holland added. "Does that help because the Bush 'brand name' is well known, or hurt because Jeb would be judged by the public based on things he did not do himself? Historically speaking, there is no way to tell."
But GOP strategist and CNN contributor Ana Navarro said Jeb Bush is free of the Bush fatigue, at least among Republicans.
"I think the Bush fatigue doesn't apply to Jeb. And even if it did, among Republicans it's been replaced with Obama fatigue," said Navarro, a longtime friend and supporter of the former Florida governor.
If Bush does decide to run, and were he to win the 2016 GOP nomination, he could face off in the general election against a member of another famous political family -- Hillary Clinton.
While the former first lady, senator, presidential candidate and secretary of state says she has no plans to run again for the White House, she hasn't ruled out a bid, and if she did run, she'd be the early favorite to win her party's nomination.
And if Bush doesn't run, there's the chance we could see a future White House bid from the next generation of the Bush family. Both of Bush's sons are considering runs for public office.
Bush told CNN that he now understands what his father went through.
"I know what my dad feels like, why he would get emotional every time he was in a setting where George or I were in pursuit of some office of some kind."