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However, perceptions shifted on Sunday when his son, George P. Bush, said his father was "moving forward" with a 2016 bid.
"I think it's more than likely that he's giving this a serious thought," his son, who is running for office in Texas, said on ABC's "This Week."
Along with his son's comments, several other signs point to Bush seriously considering a run for the White House. In September, the Wall Street Journal reported Bush's inner circle has been quietly telling top Republicans to avoid committing to other 2016 candidates. In October, Bush said his wife is actually "supportive." Bush has also ramped up his efforts on behalf of GOP candidates in this year's midterm elections. And, as recently as Tuesday, Bush was taking shots at President Barack Obama's leadership on the Ebola crisis.
According to The Tennessean, Bush also commented on his potential 2016 campaign at the same Tuesday event where he took shots at the president. Bush said he would spend a few months discussing it with his family before following "what's in my heart."
"I'm not like really freaking out about this decision, to be honest with you," Bush said.
If Bush does run, he'll shake up the 2016 field. The brother and son of the two most recent GOP presidents, Bush would likely absorb much of the political establishment's support. Furthermore, his stances on the issues generally align with the business-oriented establishment over the Tea Party when the two are in conflict.
Foreign Policy
Like most Republicans, Bush has few kind words for Obama's actions overseas. At the Tuesday event, Bush reportedly called Obama's foreign policy record an "unmitigated disaster" that lacks guiding principles, especially regarding the jihadist group Islamic State (also known as ISIS).
In terms of a broader foreign policy doctrine, DefenseNews reported in April that veteran national security officials and political observers "say his philosophy seems to align more with his realist father, George H.W. Bush, than his neoconservative brother, George W. Bush."
"I think you'll see a return, if he were to get the nomination, to the old-school classic realist Republican philosophy," Larry Korb, a former Pentagon official, told the publication. "He probably would fit the mold of his father, James Baker, and Henry Kissinger."
Taxes
Bush isn't an absolutist on tax increases. According to the Washington Times, Bush said in 2012 he could accept a fiscal deal that included $1 in tax increases for every $10 in spending cuts - a position that could get him hammered in a charged Republican primary. In response, Bush's spokeswoman issued a statement to the Times defending his record.
"As Florida's chief executive, Gov. Bush cut taxes by more than $19 billion dollars for families and businesses. At the same time, budget reserves in the state rose from $1.3 billion in 1998 to $9.8 billion in 2006," she said. "His record on cutting taxes and exercising strong fiscal discipline speaks for itself."
Education
Bush has spent much of his post-gubernatorial career focused on on education reform through the nonprofit Foundation for Excellence in Education, which he chairs. The nonprofit backs a "reform agenda" that includes, among other things, access to charter schools, outcome-based funding, and "rigorous academic standards, such as the Common Core State Standards." Common Core has been fiercely criticized by some conservatives as an intrusion by the federal government.
"We need a system driven from the bottom-up by families, a system that is organized around the individual success of each and every student. We need a system that recognizes and rewards incredible teachers, and ensures they are in classrooms with students who most need their skills," Bush said in an October press release from his nonprofit.
Immigration
Bush's biggest deviation from the modern Republican brand, however, may come on the issue of immigration. Notably, according to PolitiFact, Bush has said "conflicting things over time about eventual citizenship for illegal immigrants."
"You have to deal with this issue. You can't ignore it. And so, either a path to citizenship, which I would support and that does put me probably out of the mainstream of most conservatives; Or a path to legalization, a path to residency of some kind," Bush said in 2012. However, in his subsequent book, Bush reportedly backed off on the citizenship issue.
Regardless, Bush has struck a moderate tone on immigration. After the recent crisis of tens of thousands of unaccompanied minors crossing the US-Mexican border, Bush urged his party to avoid using that controversy as an "excuse" to delay on comprehensive reform.
Social Issues
Bush appears to more or less have adopted the standard Republican platform on social issues like abortion and same-sex marriages.
In 2006, Bush said he was leaning towards constitutional a ban on gay marriages, after previously arguing it was unnecessary, according to the Orlando Sentinel. However, Bush has not been harsh in his recent rhetoric, reportedly saying in 2013, "If people love their children with all their heart and soul and that's what they do and that's how they organize their life that should be held up as examples for others to follow because we need it."
On abortion, RealClearPolitics reported that, as governor, Bush further supported a controversial "choose life" specialty license plate and "made headlines by asking a circuit court to appoint a representative for the fetus of a mentally disabled rape victim." Even more prominently, that same year, Bush inserted himself into the debate over euthanasia by pushing for doctors to keep vegetative patient Terry Schiavo on life support.
Overall
In a presidential campaign that is already shaping up to be a debate between different factions of the Republican Party - notably the Tea Party firebrand