WASHINGTON » When former Gov. Jeb Bush of Florida quietly visited Sen. John McCain in his Capitol Hill office this fall, discussion turned to a subject of increasing interest to Bush: how to run for president without pandering to the party’s conservative base.

"I just said to him, ‘I think if you look back, despite the far right’s complaints, it is the centrist that wins the nomination,’" McCain, R-Ariz., said he told Bush.

In the past few weeks, Bush has moved toward a run for the White House. His family’s resistance has receded. His advisers are seeking staff. And the former governor is even slimming down, shedding about 15 pounds thanks to frequent swimming and personal training sessions after a knee operation last year.

But before pursuing the presidency, Bush, 61, is grappling with the central question of whether he can prevail in a grueling primary battle without shifting his positions or altering his persona to satisfy his party’s hard-liners. In conversations with donors, friends and advisers, he is discussing whether he can navigate, and avoid being tripped up by, the conservative Republican base.

"It’s now about a realistic assessment of whether the journey he wants to travel is compatible with winning a primary," said Al Cardenas, a longtime friend who was the Florida Republican Party chairman when Bush was governor.

Though he is deeply conservative on some issues such as taxes and abortion, in other ways, Bush — culturally and philosophically — is out of step with the grass-roots activists who now animate the party. He has unabashedly pushed Republicans to find consensus with Democrats, especially on fiscal issues. He has pushed for an immigration overhaul that would include a path to citizenship for people who are here illegally, and he has championed the Common Core educational standards, two incendiary issues among Republican activists, many of whom oppose both.

The governor’s decision will have significant consequences for the Republican Party. If he goes forward with a campaign in which he avoids trying to appease the most conservative voters and wins the nomination as well as the presidency, it could reshape Republican politics for a generation. Should he take that approach and lose the nomination to a more aggressive conservative, however, it would send a powerful message that a more pragmatic approach has little appeal among the party’s primary voters.

The party’s establishment elites and some longtime advisers to Bush are urging him to remain steadfast on his positions, especially on immigration, if he runs. They are convinced that Mitt Romney ruined his chance to win in fall 2012 by veering too far to the right during the primaries, turning off general election voters as a result.

"I think that, unfortunately, we saw a lot of that in the last go-round," James A. Baker III, the longtime Bush family friend and former secretary of state, said about Romney’s 2012 campaign.

"I think people are ready for somebody honest, frank and willing to tell them what they think," said Baker, adding of Bush, "I think he could run in a primary where he’s true to himself, his values and policy positions."

That is the campaign that Bush’s small inner circle is hoping he will run.

"We often say, ‘Let Jeb be Jeb,’" is how Mike Murphy, a longtime adviser, put it.

Bush seemed to be musing on such an approach last week before a gathering of chief executives in Washington, when he said that a Republican hopeful had to be willing to risk the nomination in order to remain competitive in November. "Lose the primary to win the general without violating your principles," Bush said at the event, sponsored by The Wall Street Journal.

But pursuing such an unapologetic bid — and not being pulled into "the vortex," as Bush describes it — may prove easier in theory. And Bush, having watched politics close up since he was in his 20s working on his father’s 1980 presidential campaign, understands this reality.

Speaking last month to a Republican donor, he discussed the difficulties posed by the early states in the nominating process, especially Iowa, where religious conservatives have won the past two Republican presidential contests.

"He said he knows Iowa is going to be tough," recounted the donor, who spoke on the condition of anonymity to share a private conversation. "He even joked, ‘I could probably do better there not even visiting.’"

But Gov. Terry E. Branstad of Iowa, a six-term Republican from the establishment wing of the party, said Bush could do well in the state if he committed to it, and urged him to "run a primary campaign that focuses on the general election."

Still, Branstad suggested that Bush would have to make some calibrations to his message on an education overhaul. Many conservatives fear that Common Core, the set of voluntary education standards devised by a bipartisan group of governors, could lead to a national curriculum drawn up by the federal government.

A Gallup poll in September revealed that 58 percent of Republican parents had a negative view of Common Core, up from 42 percent in the spring. The fall poll showed that just 19 percent of Republican parents view the standards favorably.

"He’s got a great record on that, but he needs to keep the focus on the substance of what he accomplished and what he thinks should be accomplished for the country, and not be defending Common Core," Branstad said.

In a speech last month to his education foundation, Bush did not back down from his support of the education standards, but he did purposefully note that nobody in the debate "has a bad motive." The question looming, should he run, is whether he would withstand pressure to move beyond that — and if doing so would undermine the sort of truth-telling campaign he would like to run.

The former governor may be able to defuse the conflict over the Common Core if he is willing to embrace conservative positions on other issues, much as his brother George W. Bush did in 2000.

Russell D. Moore, a senior leader of the Southern Baptist Convention, visited Jeb Bush at his Miami-area office this year and came away believing that Bush, who converted to Catholicism in the 1990s, "wasn’t embarrassed" about his opposition to abortion and same-sex marriage.

"This is no Jon Huntsman," he said, referring to the former Utah governor who ran as a moderate for the Republican nomination in 2012.

"But it depends on what he’s planning to do," Moore continued. "If he articulates the views he articulated to me on those issues, then that’s not backing away from social conservatism."

Bush also must grapple with his brother’s legacy, the challenge of which was illustrated this week with the release of the Senate report on the CIA’s interrogation techniques.

Bush has said that he will make a decision on whether to run by the end of this month. Yet even as he reaches out to donors and as his advisers contact potential strategists — including in early primary states like South Carolina — Bush’s business activities suggest that he is just as focused on making money as planning a campaign.

Some of his supporters grumbled this week about a Bloomberg Businessweek article about his ties to private equity, fretting that it would worry donors about how serious he was about the race. Bush’s aides swiftly pushed back against the article, arguing that it overstated the political significance of Bush’s business activities. They pointed out that the main investment company where he is a partner was established in 2008.

Many of the party’s leading officials believe he is gearing up to run — and that assumption is beginning to shape the field. When Sen. Rob Portman, R-Ohio and a longtime Bush family friend, announced last week that he would not run for president, it was in part an admission about how difficult a bid could be if Bush enters the race.

Bush would benefit most if those Republicans who do run vie for the support of the party’s hard-liners. That would fracture the conservative base, leaving an opening for him among more moderate-leaning Republicans.

"Lock up the center and let them fight it out on the right," McCain said.