A feistier Barack Obama took on "the birthers" who smear him as he kicked off his re-election campaign in Chicago, and later showed a more aggressive side of his personality with an unintended open mike session heard by the media.

"I grew up here in Chicago. I wasn't born here," he said Thursday, drawing laughs from a supportive audience. "Just want to be clear. I was born in Hawaii."

Some of the Republicans vying to take him on next year have been zealously courting the so-called birthers, who believe Obama was born in Kenya and is not a legitimate president.

Donald Trump, the billionaire with the big hair who is leading one poll of Republican presidential contenders, said "I wanted him to show his birth certificate… there's something on that birth certificate that he doesn't like."

Hawaii officials have repeatedly confirmed Obama's citizenship, and his certification of birth in Hawaii has been made public. But that hasn't stopped Republicans such as Sarah Palin or Mike Huckabee from making comments that blur the issue.

"More power to him," said Palin of Trump's interest in Obama's birth certificate. And Huckabee has said he would "love to know more" about where Obama was born.

Doubts raised about Obama's birthplace led the Arizona senate to approve a bill Wednesday that would require presidential candidates to prove they are U.S. citizens before their names can appear on the state's ballot.

Arizona would be the first state to require the proof if the governor signs it into law, but 13 other states have considered similar legislation.

Obama has tried to address the subject with some humour. "Most people feel pretty confident the president was born where he says he was, in Hawaii [laughs]. He doesn't have horns."

Open mike catches Obama remarks

Signs that Obama's patience has its limits were apparent Thursday night in Chicago, however, when his off-the-cuff remarks near an open mike were captured by CBS News.

He had tough words for the Republican chairman of the House budget committee, Representative Paul Ryan of Wisconsin.  

"This is the same guy who voted for two wars that were unpaid for, voted for the Bush tax cuts that were unpaid for, voted for the prescription drug bill that cost as much as my health-care bill but wasn't paid for," Obama said.

Regarding Republican efforts to repeal his health-care bill, Obama said,

"You wanna repeal health care? Go at it. We'll have that debate. But you're not going to be able to do it by nickel and diming me in the budget. You think we're stupid?"

Obama, in remarks overheard by The Associated Press, also expressed frustration with the technology at his disposal.  

"The Oval Office, I always thought I was going to have really cool phones and stuff," he said during a small fundraising event at a Chicago restaurant. "I'm like, 'C'mon guys, I'm the president of the United States. Where's the fancy buttons and stuff and the big screen comes up?' It doesn't happen."  

Government information technology, he complained, is "horrible."  

"It's true in the Pentagon. It's true in the agencies. It's true in the Department of Homeland Security."

With files from the CBC's Michael Colton and The Associated Press