Washington (CNN) - It's surely not what the leader of the free world wants for his birthday. But, for a stubborn group of Americans, conspiracy theories about President Obama's birthplace are the gifts that keep on giving.

The president celebrates his 49th birthday Wednesday. On the same day, a new national poll indicates some Americans continue to doubt the president was born in the United States. According to a CNN/Opinion Research Corporation survey, more than a quarter of the public have doubts about Obama's citizenship, with 11 percent saying Obama was definitely not born in the United States and another 16 percent saying the president was probably not born in the country.

Full results [pdf]

Forty-two percent of those questioned say they have absolutely no doubts that the president was born in the U.S., while 29-percent say he "probably" was.

"Not surprisingly, there are big partisan differences, although a majority of Republicans thinks Obama was definitely or probably born here," says CNN Polling Director Keating Holland. "Eighty-five percent of Democrats say that Obama was definitely or probably born in the U.S., compared to 68 percent of independents and 57 percent of Republicans. Twenty-seven percent of Republicans say he was probably not born here, and another 14 percent of Republicans say he was definitely not born in the U.S."

The theory that the president was not born in the U.S. has nagged him since the 2008 presidential campaign. A group of true believers, known as "Birthers," have pressed the idea that Obama was born in another country - some say in his father's homeland of Kenya. By their claims, Obama is constitutionally ineligible to serve as president.

On the president's birthday, some websites bent on advancing the theory are wishing Obama a "Happy Birther Day." And some of the president's staunchest critics are fanning the flames.

On Tuesday, conservative radio talk show host Rush Limbaugh quipped on his program, "They tell us August 4th is the birthday. We haven't seen any proof of that!"

Yet there is ample evidence that defies Limbaugh's statement and the beliefs of the 27-percent of Americans that, according to the poll, doubt the president's birthplace. CNN and other news organizations have thoroughly debunked the rumors.

Hawaii has released a copy of the president's birth certificate - officially called a "certificate of live birth." And in 1961 the hospital where the president was born placed announcements in two Hawaiian newspapers regarding Obama's birth.

The White House has called doubts that Obama was born in Hawaii "fictional nonsense."

But questions persist. So much that in May, Hawaii passed a law that allows state agencies to ignore repeated requests to view government records, including the president's birth document. Hawaii's Republican Gov. Linda Lingle signed the legislation into law.

Around that time, Lingle - who campaigned for Sen. John McCain and Sarah Palin in 2008 - criticized questions about the president's birth.

In a WABC interview before signing the legislation, Lingle said, "...I had my health director, who is a physician by background, go personally view the birth certificate in the birth records of the Department of Health." Lingle added, " ? The president was in fact born at Kapi'olani Hospital in Honolulu, Hawaii. And that's just a fact."

"It's been established he was born here," the governor continued. "I can understand why people want to make certain that the constitutional requirement of being a, you know, natural born American citizen ? but the question has been asked and answered. And I think just we should all move on now."

The CNN/Opinion Research Corporation poll was conducted July 16-21, with 1,018 adult Americans questioned by telephone. The survey's overall sampling error is plus or minus three percentage points.

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