– Amid growing public opposition, the Honolulu City Council recently dropped a proposal to rename a popular beach in honor of President Obama. Last year, Hawaii’s Legislature adjourned without acting on a bill that would designate the president’s birthday as a state holiday. To this day, would-be landmarks such as the apartments where Obama lived are without tangible tributes to the man many here once knew simply as Barry.

Despite the immense pride Hawaiians profess about Obama’s historic rise to the presidency, there are few, if any, markers to call attention to his roots.

“It’s not like you’re going to Mount Vernon,” quipped Democratic Sen. Brian Schatz, contrasting the plantation home of the nation’s first president with a high-rise former residence of its current one.

But what would seem like indifference toward marking Obama’s time here is instead the apparent result of a combination of the state’s humble character and the respect locals say they have for Obama. What they await is a sign of whether Obama returns the affection.

Though Obama just concluded two weeks of what has become the first family’s traditional vacation here, such trips increasingly appear less like homecomings. Obama attends luaus and plays golf with old friends, but he and his family stay at a rented home. He hasn’t lived here since he left for college, and few expect him to return full time when he leaves the White House. He only occasionally interacts with the public, and doesn’t return to the sites of childhood exploits.

Residents mostly leave him alone, yet see him as one of their own.

“It doesn’t matter where you live. It’s where your heart is,” said Mira Secretaria, who was buying a birthday cake recently at the Baskin-Robbins where Obama worked as a teenager, just blocks from the hospital where he was born and two of the apartments he spent time in as a child. “I never thought of him as from the mainland.”

The debate about Hawaii’s place in Obama’s story is part of a larger one that’s playing out as Obama stares down what he calls the “fourth quarter” of his time in office.

Here, says Neil Abercrombie, the former governor and longtime congressman, Obama’s experiences formulated his values.

“The very foundation of the president’s worldview is of Hawaii and the aloha spirit,” said Abercrombie, who boasts perhaps the longest connection to the president, having attended graduate school here with Obama’s father. While Obama’s career is undeniably linked with Chicago, his identity is grounded in Hawaii, Abercrombie said.

“He is entirely comfortable here, and I’m confident that, in terms of his personal references post-presidency, Hawaii will always occupy a central place in his heart,” he said.

One clear signal of how Obama views Hawaii will come this year when he and the first lady choose the site of his presidential library. Potential hosts include Honolulu as well as New York and his adopted home of Chicago.

In December, Hawaii leaders delivered their vision for an “action-oriented” presidential center on prime waterfront real estate in the Kaka’ako neighborhood of Honolulu that would help serve as a catalyst for the kind of busy ex-president they expect Obama to be.

“Our conception of the presidential center is to have it enable activity rather than stand as a monument,” said Schatz, the chief public booster of Hawaii’s bid. “Part of that is because of Hawaii’s culture, and part of that is understanding that President Obama is going to be in his early 50s [when he leaves office]. I don’t think he wants a museum or statue in his name. I think he wants to continue to be engaged.”

Officials involved in the museum bid say their plans could be adapted whether or not Obama chooses the state as primary host of his archive. That’s a tacit concession of their bid’s underdog status, one they hope to overcome with a sentimental connection others can’t match.

“Understanding President Obama requires that you understand Hawaii; it requires that you understand tolerance and multiculturalism. And therefore when the president comes to making this unique and singular … decision, I don’t think it’s going to come down to a traditional analysis of who’s got more juice,” Schatz said.

Many here say that tributes are not in keeping with Hawaii’s character. Honolulu law bars, for the moment, naming public structures in honor of living people. The weight of the label of birthplace of a president could change that, though.

“He never really forgot that he grew up in Hawaii, and it shaped him,” Kevin Mizuno, 47, said over an ice cream cone at the Baskin-Robbins. There is no sign yet denoting that Obama worked there.