The White House says the hug-promised-'round-the-world between President Obama and Hillary Clinton won't be anything new for the former colleagues and rivals, but it probably won't be public.

Eighteen months after Clinton left Obama's service as secretary of state, she caused a stir by criticizing elements of his foreign policy in an interview with The Atlantic's Jeffrey Goldberg.

Clinton's office tried to make light of the kerfuffle by saying the two were planning on "hugging it out" when they saw it each other at a mutual friend's birthday party in Martha's Vineyard.

The White House went along with that on Wednesday, downplaying their differences and reminding reporters that Obama and Clinton had a "close and resilient relationship."

"I believe the president and Secretary Clinton have had many hugs over the last few years," White House spokesman Eric Schultz said Wednesday at a briefing from Martha's Vineyard, where Obama is vacationing with his family.

However, Schultz said the media wouldn't get to witness the reunion. "I appreciate the request, but I do think this is a private social gathering for someone’s birthday, so it’s going to be hard to bring all of you lovely people in," he said.

The relationship between Obama and Clinton is perhaps the most closely-scrutinized in American politics, ever since the new president tapped his former rival to serve as secretary of state following his election in 2008. That dynamic will only be heightened as Clinton prepares for a possible bid to succeed Obama in 2016.

In the Atlantic interview, Clinton criticized Obama's "Don't do stupid stuff" description of his foreign policy goals, and she said the "failure" to sufficiently aid Syrian rebels had left a vacuum that the Islamic State of Iraq and the Levant had then filled.

Clinton had advocated within the administration for arming the rebels, but she lost the internal battle – a point she described in her book, Hard Choices.

"We know that was an honest policy difference," Schultz said "don't do stupid stuff" encapsulated Obama's foreign policy, saying no one at the White House would describe it that way.

That was a more diplomatic reply than the brush-back pitch thrown Tuesday by Obama's longtime political adviser, David Axelrod, who had responded to Clinton's criticism on Twitter in a thinly-veiled jab at her vote for the Iraq war:

Clinton called Obama to emphasize that her comments in the article were not meant as criticism, and Schultz said the president "appreciated her call" and looked forward to seeing her on Wednesday night.

He said Obama "values her opinion" while acknowledging they had occasional "small policy differences."

Still, the world may never get to see Clinton and Obama hug it out on Wednesday, as Schultz wouldn't guarantee there would be photos from a private party.