Donald Trump Donald John TrumpObama calls on Senate not to fill Ginsburg's vacancy until after election Planned Parenthood: 'The fate of our rights' depends on Ginsburg replacement Progressive group to spend M in ad campaign on Supreme Court vacancy MORE is set to shift his strategy to win the White House, becoming less antagonistic toward the GOP establishment and adopting a less abrasive tone on social issues. But the approach brings risks as well as potential rewards.

At a closed-door briefing with Republican National Committee (RNC) members Thursday, Trump aide Paul Manafort assured his audience that his boss is not “running against” the national party and that he “cares about the united team.”

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In his remarks, first reported by The New York Times, Manafort also raised eyebrows by saying of Trump, “the part he’s been playing is evolving.”

But Trump will have to tread a fine line, as comments he made at the weekend acknowledged. At a Saturday rally in Waterbury, Conn., Trump suggested that he would never have reached his current position as the dominant GOP front-runner had he "acted presidential" from the outset of his campaign.

The key question is whether Trump can establish more civil relations with the RNC and set a more sober-minded tone in general — while also not disenchanting supporters who were drawn to the businessman as a brash voice unwilling to pay deference to the powers-that-be.

Manafort’s comment about Trump playing a part could also raise doubts about his sincerity, echoing a 2012 comment from an advisor to GOP nominee Mitt Romney that, after the primary had been won, Romney’s approach could be changed like “an Etch A Sketch.”

On social issues, Trump raised eyebrows with some conservatives when he suggested he was opposed to North Carolina’s controversial “bathroom law” requiring transgender people to use the restroom of their original gender.

Originally, speaking to NBC’s “Today” show, Trump said there was no real need for the law, arguing that “there have been very few complaints the way it is.” Trump finessed that point later that day, telling Fox News Channel’s Sean Hannity that “local communities and states should make the decision.”

Trump will give a major foreign policy speech at the Mayflower Hotel in Washington on Wednesday. He is expected to use the occasion to present a more statesman-like approach to a candidacy that has so far been characterized by controversial stances on illegal immigration, Muslims and a host of other issues.

Some commentators are less than thrilled with the new version of Trump — and they are blaming Manafort and other recent additions to his team.

“I wish Trump would go back to retweeting juvenile photos of Heidi Cruz,” pundit Ann Coulter tweeted on Friday. “I hate the new Manafort & Black Trump.”

(“Manafort & Black” alludes to a Washington lobbying firm in which Manafort and another scion of the GOP establishment, Charlie Black, were principals. The company has not had that name since a merger in the 1990s.)

In Connecticut on Saturday, Trump insisted he does not plan to start "toning it down." He also said, “You know, being presidential’s easy — much easier than what I have to do. Here, I have to rant and rave. I have to keep people going. Otherwise you’re going to fall asleep on me, right?”

Most Republican strategists believe that there is an imperative for Trump to tack toward the center and try to unify the party, however.

“I don’t know if Trump is playing a part but he certainly needs a second act,” said GOP strategist Ford O’Connell. “Cozying up to the GOP establishment is risky because it could conceivably reinvigorate the Never Trump crew. Nevertheless, it’s the right thing to do if he wants to win the general election.”

The GOP establishment is welcoming Trump’s overtures. RNC chairman Reince Priebus told the Washington Post on Friday: “Donald Trump is conciliatory. You notice he hasn’t been saying ‘RNC’ lately. He hasn’t been saying that lately. He certainly hasn’t been talking about me lately.”

The same day, Priebus had slammed the Never Trump movement, insisting that “it is essential to victory in November that we all support our candidate” and adding, “politics is a team sport, and we can’t win unless we rally around whoever becomes our nominee.”

GOP strategist Matt Mackowiak said that those statements “made sense from [Priebus’s] perspective” since he has to support the nominee, whoever that is. But Mackowiak also said that the statement “felt like it might have been the result of some outreach [the Trump campaign] may have been making to the RNC.”

Mackowiak, however, suggested that political risk for Trump resided less in easing off his confrontations with the RNC and more in statements such as his one about the North Carolina bathroom law.

“It just reinforces the idea that he is not the full-throated conservative that he says he is,” the strategist said.

Trump's most serious rival for the GOP nomination, Texas Sen. Ted Cruz Rafael (Ted) Edward CruzSenate Republicans face tough decision on replacing Ginsburg Cruz: Trump should nominate a Supreme Court justice next week Renewed focus on Trump's Supreme Court list after Ginsburg's death MORE, has seized on the comments about the North Carolina law. Cruz's campaign released an ad highlighting what Trump had said. At a campaign event in Frederick, Md., on Thursday, the senator cited the remarks as a "stark illustration" of why conservatives should not vote for the business mogul.

Mackowiak and O’Connell also independently questioned whether Trump would have the restraint to stick to a more reserved, statesman-like tenor.

That question was heightened even before his remarks in Connecticut on Saturday. At an earlier event, on Friday afternoon, Trump appeared to mimic an Indian accent when discussing a call he had made to a foreign-based call center.

“He already had the image of the fighter who won’t back down, down pat,” said O’Connell. “He has to start demonstrating that he has the steady hand of presidential leadership. The tone and rhetoric is better. But does he have the discipline? We don’t know.”