Last year family matriarch Barbara Bush proclaimed there have been “enough Bushes” in the White House, but recently son Jeb unambiguously revived prospects of extending the political dynasty.
In his most elaborate discussion yet on the matter of 2016, the popular two-term Republican governor of Florida sent a jolt through the political chattering class by promising he will decide by year's end whether he will run, and by laying out what a possible Jeb Bush candidacy might look like.
At an event marking the 25th anniversary of his father George Bush's presidency, the second son discussed his own prospective campaign - an “optimistic” challenge to today's rough-and-tumble politics that have marred recent Republican nominating contests.
Should he run, Bush said on Sunday at his father's presidential library, he would not get drawn “back into the vortex of the mud fight”.
While core conservatives like Senator Ted Cruz, a putative 2016 rival, have argued that Republicans must nominate the most conservative electable candidate, Bush takes the middle road.
He encourages fiscal prudence while defying party orthodoxy on issues like immigration and supporting national educational standards panned by the right wing.
“Campaigns ought to be about listening and learning and getting better,” he said. “I do think we've lost our way.”
In short, he seeks a broader Republican vision “organised around winning the election, not making a point”, he said, signalling he won't demand ideological purity that can rally the base but doom the party in national contests.
“Jeb Bush is suddenly becoming interesting,” Steffen Schmidt, professor of political science at Iowa State University, told AFP.
He said Bush is showing political adeptness that some conservatives lack. And with New Jersey Governor Chris Christie hamstrung by scandal, Bush is emerging as a leading Republican centrist.
In particular Bush called on Sunday for greater compassion for America's illegal immigrants, who he said enter the United States to “provide for their families”.
“Yes, they broke the law. But it's not a felony, it's an act of love,” Bush said.
The remark reverberated throughout Washington, where Jeb, 61, is being carefully watched - and perhaps courted. Lawmakers admire his extensive political network and recognise the potential of a Republican with the gravitas to become a beacon for conservatives, moderates and independents alike.
“He's a very attractive candidate,” Republican Senator Lindsey Graham said.
Senator John McCain, the 2008 Republican nominee, said he appreciates that Jeb seeks an immigration policy overhaul, after brother George W. Bush ran into headwinds with related reforms during his presidency.
Yet “it's too early, it's a crowded field, and I don't even know if he's running”, McCain said. “But I've always respected him.”
Schmidt noted Bush would face conservatives like Mike Huckabee and Rick Santorum, who both ran in 2012 and drew many nominating races far to the right.
That forced Mitt Romney to embrace deeply conservative positions from which he struggled to recover after winning that year's Republican nomination, and he lost to incumbent Barack Obama.
Bush could face similar challenges in early 2016 primaries.
“You can be popular nationally and the mainstream media can love you, but if you can't win Republican primaries in Iowa... New Hampshire or South Carolina, you can't win the nomination,” said Brown University associate professor Wendy Schiller.
Another hurdle: Tea Party groups that advocate slashing spending and Libertarians opposed to military adventurism might not separate Jeb from George.
“They weren't in love with George W. Bush because of the debt and wars, and I don't see how Jeb Bush escapes that,” Schiller said.
As the son and brother of presidents, Jeb Bush would be propelled and saddled by his famous name - although the same could be said in the case of Hillary Clinton, the former secretary of state and White House first lady who herself is the presumptive Democratic frontrunner for 2016.
The Bush name is a successful Republican brand for many. But critics argue it could be his Achilles heel, symbolising neo-conservative war-mongering.
“Much of the country has Bush fatigue, and the idea of Bush 3.0 or another Bush-Clinton matchup would be a bit much,” said Robert Watson, professor of American studies at Florida's Lynn University, which hosted an Obama-Romney debate in 2012.
“Yet he's a legitimate candidate. Folks down here are constantly talking about him.” - Sapa-AFP