In the birther movement, Mr. Trump recognized an opportunity to connect with the electorate over an issue many considered taboo: the discomfort, in some quarters of American society, with the election of the nation’s first black president. He harnessed it for political gain, beginning his connection with the largely white Republican base that, in his 2016 campaign, helped clinch his party’s nomination.
The more Mr. Trump questioned the legitimacy of Mr. Obama’s presidency, the better he performed in the early polls of the 2012 Republican field, springing from fifth place to a virtual tie for first.
That frenzied period culminated six weeks after it began in a surreal televised split screen between Mr. Trump and the White House briefing room, where aides released an image of the president’s birth certificate proving he was born in Honolulu and Mr. Obama directly addressed the issue.
It was a remarkable moment that Mr. Trump celebrated as a political victory.
Then Mr. Trump did something decidedly un-Trump-like: He dropped the issue and rarely spoke of it publicly again.
According to people apprised of the conversations, people close to him had been worried about the negative attention. Officials at NBC had also been concerned that he was alienating the large black audience of his hit show, “The Apprentice.”
But for all of his fascination with the president’s birth certificate, Mr. Trump apparently never dispatched investigators or made much of an effort to find the documents.
Dr. Alvin Onaka, the Hawaii state registrar who handled queries about Mr. Obama, said recently through a spokeswoman that he had no evidence or recollection of Mr. Trump or any of his representatives ever requesting the records from the Hawaii State Department of Health. NYTimes