Former Secretary of State Hillary Rodham Clinton holds her book "Hard Choices" Wednesday at Bunch of Grapes Bookstore on Martha's Vineyard. (Steven Senne/AP)

Hillary Rodham Clinton swept onto Martha’s Vineyard on Wednesday amid torrential downpours — and a torrent of speculation ahead of her first meeting with President Obama after she criticized his foreign policy earlier this week.

And if the skies hadn’t exactly cleared over the island, the Clinton and Obama camps insisted that the storm clouds that seemed to loom over the relationship between the two after her comments in an interview with the Atlantic had parted.

At Clinton’s first stop, the Bunch of Grapes Bookstore, hundreds lined up outside for hours in the rain to meet the former secretary of state. They heard a brief explanation of her interview comments — and a personal confirmation that she would, as her spokesman had promised, “hug it out” with Obama at a party later that night.

“Absolutely,” Clinton said, when asked about the much-anticipated embrace. “Yeah. Looking forward to it. Going to be there tonight.”

Clinton said the decision to call Obama after the interview to apologize wasn’t a difficult one.

“We agree,” she said. “We are committed to the values and the interests of the security of our country together. We have disagreements as any partners and friends, as we are, might very well have.”

Obama has articulated his foreign policy as such: Don’t do stupid stuff. Clinton said in the Atlantic interview that it wasn’t enough.

“Great nations need organizing principles, and ‘Don’t do stupid stuff’ is not an organizing principle,” she said.

Asked at the bookstore Wednesday whether she disagrees with Obama’s policy on Iraq, Clinton switched gears and said, “I’m excited about signing books.”

That would seem to be a prerequisite for an event like this one: The bookstore said it had ordered 1,000 copies of “Hard Choices,” the number Clinton’s people have said she can sign in two hours. Clinton, wearing a dusty-rose-colored textured jacket, greeted people who shuffled by the table where she was signing. As each person — many of them in ponchos and with soaking wet hair — filed by, an aide slid a copy of “Hard Choices” to Clinton, the front cover open.

“I’ll be voting for you,” a woman said to the prospective 2016 presidential candidate.

“Bless your heart,” she replied.

Clinton made small talk about Martha’s Vineyard, telling one attendee that she is “not here long enough,” and trying to get a high-five out of 6-year-old Audrey Lamb-Wilson when the girl wouldn’t take a photo with her. Audrey obliged.

“Thank you for coming, staying out in the rain,” Clinton told the crowd, some of whom wore “Ready for Hillary” stickers.

“The potential to meet the first woman president of the United States,” said Audrey’s mother, Alycia Lamb of Seattle. “It’s pretty monumental.”

Quentin Heyward of Philadelphia shuffled toward the exit after meeting Clinton, who he said had “reenergized” him.

“She is the Merkel of the Americas,” Heyward said, referring to German Chancellor Angela Merkel. “She’s cutting edge, she’s respected, she’s trusted.”

There was little mention of the other major political figure on the island: Obama, here for a two-week vacation.

Over the days since Clinton’s initial comments, speculation in Washington has run rampant: How would Obama respond? Would it affect their relationship? Are they friends or enemies — or a bit of both? And exactly how awkward would their first post-comment meeting, and the promised Hug of Reconciliation, really be?

“Pool reporter better get in there with a tape measure to determine official hug distance,” Democratic strategist Donna Brazile tweeted in the hours before the event. “We have a right to know. Agree? #huganalysis”

The frenzy over Clinton’s comments, and anticipated embrace, reached fever pitch at the White House news briefing Wednesday, where reporters pressed deputy White House press secretary Eric Schultz on the state of the Obama-Clinton relationship — and pushed for access to the pair’s rapprochement.

“They have a close and resilient relationship,” insisted Schultz, who added that Obama had “appreciated” Clinton’s call. “I’m not sure anyone in this room would contest that [not] doing stupid stuff is a good idea, but I also don’t think anyone at the White House would assert that that is the — how we would describe our approach to foreign policy.”

Schultz did concede that Obama and Clinton have disagreed on several fronts, including whether and when to arm Syrian rebels — but he played down the distance between them.

“They continue to agree on a broad majority of issues confronting our country, even if they have the occasional policy difference,” Schultz said.

As to the hugging: No big deal, he insisted — the two have been there before.

“I believe the president and Secretary Clinton have had many hugs over the past few years,” Schultz said, informing reporters that the latest embrace would go undocumented. “I suspect many of them have been caught on camera.”