Jeb Bush, left, was a guest on Mitt Romney’s plane during Romney’s 2012 presidential campaign, along with Sen. Marco Rubio, foreground right, and then-Rep. Connie Mack, foreground left. (Melina Mara/The Washington Post)

Jeb Bush and Mitt Romney have much in common. Both were pragmatic as governors, mild-mannered as candidates and more comfortable balancing budgets at their desks than clinking glasses at a political dinner.

The two Republican leaders’ personal rapport is cordial. But they are hardly chummy — and at moments their relationship has been strained, with each man’s intertwined political network carrying some grievances with the other’s.

As Bush, 61, and Romney, 67, explore presidential campaigns in 2016, they are like boxers warming up for what could become a brutal bout, sizing each other up and mulling whether or when to step into the ring.

Their early maneuvering reveals a level of competitiveness and snippiness that stems from a long history following similar career paths in business and politics prescribed by their dynastic families.

“We’re seeing the first shots of the war between clan Romney and clan Bush,” said Alex Castellanos, a Republican strategist who has worked for both men. “Both bring to the battle incredibly powerful fan clubs as well as wounds they have to heal. How ugly could it get? You’re only competing to lead the free world.”

Could the third time be a charm for Mitt Romney? The former Republican presidential candidate is making moves to explore another possible White House bid, according to sources. The Post's Karen Tumulty explains what's happening behind the scenes, and what it could mean for the 2016 GOP field. (Julie Percha/The Washington Post)

Bush has been trying to consolidate support among establishment donors, leaders and operatives since announcing in December that he would begin laying the groundwork for a likely campaign.

“The Bush connection is a centrifugal force, and it’s drawing back a whole generation of public servants and politicos,” said former Utah governor Jon Huntsman, one of Romney’s 2012 opponents.

But on Friday, Romney sought to slam the brakes on Bush, telling about 30 powerful donors that he, too, was seriously considering a 2016 bid. “I want to be president,” he said, adding that his wife, Ann, was supportive.

Romney has begun methodically calling donors, staff members and endorsers from his two prior campaigns to measure how deep his reservoir of support would be if he runs for a third time, his advisers said. He also has scheduled a series of public speeches, including a Jan. 28 address at Mississippi State University.

The entry of both Bush and Romney is far from certain, and Romney’s dalliance is preliminary. But the prospect of two center-right heavyweights entering a 2016 field likely to be fluid, crowded and diverse forces other contenders and the party’s stable of donors to adjust their thinking.

“Awkward,” was the reaction from several past Romney supporters when they learned he was weighing a 2016 campaign. If both he and Bush run, they would occupy similar space as favorites of the party brass and business community.

“The abundance of great candidates developing on the Republican side is making life very tough for me because I’m going to have to choose amongst friends,” said former New Hampshire governor John H. Sununu, who was White House chief of staff under Bush’s father but a top campaign surrogate for Romney.

But, Sununu added, “it’s applesauce right now. Let’s not try to pick up applesauce and move it to the other side of the plate.”

More personal race

The two candidates would invite comparisons to each other, which could be tense for Bush, who was sharply critical of Romney’s 2012 campaign — in particular, his lack of outreach to minorities — and has pledged to run a more inclusive and transparent campaign.

“A Romney-Bush race could end up being nastier than Jeb against someone like Ted Cruz or Rand Paul,” Bill Kristol, editor of the Weekly Standard, said of the Texas and Kentucky senators. “A Cruz-Bush race is pretty straightforward and ideological. A Romney-Bush race would be more personal — about whose turn it is and who is owed it.”

Associates of both men insist there is no animosity between them and that each will make his decision about a 2016 run irrespective of the other.

“Governor Bush respects Governor Romney,” said Bush spokeswoman Kristy Campbell, who worked on Romney’s 2012 campaign. “His process moving forward won’t be impacted by Governor Romney’s decision to explore a run — and I would assume it is the same on the reverse side.”

Beth Myers, a longtime adviser to Romney, said he and Bush have been friends since 2002, when Romney was elected to his first term as Massachusetts governor and Bush to his second as Florida governor.

“Mitt has great respect for Jeb’s ability and integrity, and they’ve worked together many times over the years to promote conservative principles,” Myers said. “At the end of the day, whatever decision Mitt makes about running for president, I’m 100 percent certain he will still value and maintain his friendship with Jeb.”

Mitt and Ann Romney also have nurtured a friendship with Bush’s parents, former president George H.W. Bush and his wife, Barbara. In 2007, when Romney gave a personal speech on his Mormon faith, which had become a touchy issue with evangelical Christian voters, he did so at the George Bush Presidential Library in College Station, Tex., where he was warmly introduced by the 41st president.

Working on Romney’s 2008 primary campaign were several Jeb Bush lieutenants: Sally Bradshaw, Bush’s longtime political adviser; Ann Herberger, a Miami-based fundraiser; and Al Cardenas, a fixture in Florida Republican politics. All three stayed out of Romney’s 2012 campaign, although Cardenas, then the chairman of the American Conservative Union, endorsed him as the primaries were ending.

The Bush-Romney family dynamic has been one of intrigue and ambition, dating at least to the 1950s, when Romney’s father, George Romney, then president of American Motors, was striving to make political connections as he eyed a run for office.

In 1957, Romney wrote a letter to Prescott Bush, Jeb’s grandfather then serving in the Senate from Connecticut, urging him to test-drive a Rambler or a Metropolitan. Both were popular AMC models, and Romney told Bush the latter got 40 miles to the gallon, according to car-industry historian Patrick R. Foster’s book “The Metropolitan Story.” But, Foster writes, it remains unknown whether the efforts resulted in a sale — or even if Romney’s solicitation drew any notice in Bush’s office.

Eyeing one another

In recent weeks, Mitt Romney and Jeb Bush have been quietly trying to ascertain the other’s motives and playbook. Bush has asked Romney’s former donors about what Romney is up to, while Romney met shortly before Christmas with Bush strategist Mike Murphy and inquired about Bush’s preparations, according to political consultants who know Romney and Bush.

Romney has said little publicly about Bush, but in exchanges with intimates, he has focused on Bush’s past advisory work for Lehman Brothers and Barclays, two major financial institutions. He argued that it makes Bush vulnerable to the same kind of Democratic attacks that he faced in 2012 over his career as Bain Capital co-founder and chief executive. He also has voiced doubts about Bush’s political skills and ability to beat likely Democratic candidate Hillary Rodham Clinton.

Ana Navarro, a GOP operative and Bush confidant, said: “I’m not going to get worked up over comments Romney has allegedly made to donors behind closed doors — yet. We all know he sometimes misspeaks.”

Bush has vowed to more vigorously defend his business record than Romney did. Comparing their careers is like “comparing an apple to a peanut,” Bush said in a December interview with a Miami television station.

Those comments irritated Romney’s family and loyalists, who took them as a slight against his career managing a complicated enterprise on a scale far larger than Bush’s business dealings, according to Romney associates.

Bush also is considering releasing a decade or more of his tax returns after Romney faced heat for only reluctantly releasing two years of his returns. And Bush has advocated a more welcoming message on immigration reform than Romney’s hard-right position, which he criticized in 2012.

“He got sucked into other people’s agendas, and I think it hurt him a little bit,” Bush said in the TV interview. He added, “Winning with purpose, winning with meaning, winning with your integrity is what I’m trying to talk about.”

Before announcing his 2012 campaign, Romney, sensing that immigration policy would be a contentious issue in the primaries, sought Bush’s advice.

“I went to see Jeb, I flew down to see him, and said: ‘I’d like to take immigration off the issue list for the primaries. And wouldn’t it be great if Republicans could come up with an immigration plan that all of the contenders could say, yeah, I agree. And then we could sweep that aside,’ ” Romney told The Washington Post’s Dan Balz in an interview for his book “Collision 2012.”

“We were unable to get there,” Romney continued. “I mean, there just wasn’t enough consensus among Republicans generally.”

Rival strategists

As Bush and Romney explore a run, whispering into their ears are two political professionals with big egos, eccentric personalities and a long-simmering rivalry: Romney’s Stuart Stevens and Bush’s Murphy. They are fierce competitors with roots in each other’s turf. Stevens worked on George W. Bush’s presidential campaigns, while Murphy worked on Romney’s 2002 gubernatorial campaign.

Members of Bush’s team have not forgotten Stevens’s role in Bush’s 1994 gubernatorial race, which became Bush’s lowest point politically. Stevens advised one of Bush’s primary opponents, Jim Smith, who waged a bruising TV ad assault against Bush over his business experience and character.

“This begins the destruction of Jeb Bush,” Stevens told the New York Times as the ads began. Bush won the primary, but he didn’t win the governorship until four years later.

During the 2012 campaign, Murphy mocked Stevens on Twitter as Romney struggled in the primaries against relatively weak opponents. More recently, Romney backers have been murmuring fresh questions about Murphy’s work for the political action committee of former New York mayor Michael R. Bloomberg (I), who is anathema to the conservative base.

Some Romney allies are bitter that Bush was slow to endorse Romney in 2012. In the run-up to the Florida primary, with Romney fighting to beat back a surge from Newt Gingrich, Bush sat on the sidelines when Romney’s team thought he could have made a difference. Romney called, e-mailed and met privately with Bush to try to win him over, but he could not be convinced.

“I voted absentee,” Bush said on CNN. “And thank God it’s a secret ballot.”

Romney won Florida nevertheless, and by the time Bush announced his endorsement, on March 21, the day after Romney’s decisive victory in the Illinois primary, the nomination was all but officially his.

Bush called Romney on his cellphone, with no tip-off from an emissary, and their talk was brief, according to aides. Back at headquarters, advisers were pleased by the news, but grumbling still, wondering why it had taken so long.

Tom Hamburger contributed to this report.