TAMPA, Fla. -- A portrait of a humane, tender-hearted Mitt Romney emerged on Thursday at the Republican National Convention, even as he urged Americans to punish Barack Obama for his broken promises about a brighter future by voting him out of office this November.

"I accept your nomination for president of the United States," a teary-eyed Romney told cheering delegates, many of whom were long cool towards his candidacy. "I do so with humility, deeply moved by the trust you've placed in me."

Romney took aim at Obama's record, saying Americans deserved better than the president.

"Hope and change had a powerful appeal," Romney said.

"But tonight I'd ask a simple question: If you felt that excitement when you voted for Barack Obama, shouldn't you feel that way now that he's President Obama? You know there's something wrong with the kind of job he's done as president when the best feeling you had was the day you voted for him."

The prime-time speech was clearly aimed at the disaffected Obama voters tuning into the convention, rather than the thousands of like-minded Republicans gathered in Tampa, as Romney reiterated time and again: Obama is a failure.

"I wish President Obama had succeeded because I want America to succeed," Romney said.

"But his promises gave way to disappointment and division. This isn't something we have to accept. Now is the moment when we can do something, and with your help, we will do something. Now is the moment when we can stand up and say: 'I'm an American. I make my destiny. And we deserve better. My children deserve better. My family deserves better. My country deserves better."'

Romney's speech had two goals: to forcefully make the case that his private sector experience makes him the better man than Obama to pull the country out of its economic morass, and also to give wary Americans a glimpse of his heart and soul.

During her own speech at the event, Romney's wife, Ann, spoke of the tall, awkward, funny teenager she fell in love with four decades ago. His running mate, Paul Ryan, poked affectionate fun at Romney's love of "elevator music."

The big question on the convention floor all day Thursday was this: Would the 65-year-old Romney let his guard down and let Americans in?

He did his part in his high-stakes Thursday speech, the most important of his life.

"My mom and dad gave their kids the greatest gift of all -- the gift of unconditional love. They cared deeply about who we would be, and much less about what we would do," he said in his prepared remarks.

"Unconditional love is a gift that Ann and I have tried to pass on to our sons and now to our grandchildren. All the laws and legislation in the world will never heal this world like the loving hearts and arms of mothers and fathers. If every child could drift to sleep feeling wrapped in the love of their family -- and God's love -- this world would be a far more gentle and better place."

But it was the testimonials from a trio of every-day Americans personally touched by Romney's Mormon faith and kindness that were the most powerful of the entire convention, leaving the array of political speakers in their dust and many on the floor of the Tampa convention centre in tears.

An elderly Vermont couple told how Romney, acting as a lay pastor for the Mormon church, helped them deal with the terminal illness of their 14-year-old son more than 30 years ago. Romney helped the boy craft his will so that he could leave his teenaged possessions to his friends and family.

"How many men do you know would take the time out of their busy lives to visit a terminally ill 14-year-old and help him settle his affairs?" asked Pat Oparowski.

Pat Finlayson had a similar story about Romney pitching in to help her and her husband deal with the demands of a seriously ill baby, even helping to fold laundry. The girl died at 26 last year, and again, the Romney family reached out.

"In the midst of making the final decision to run for president -- which had to be the most difficult of their lives -- when they heard of Kate's passing, both Mitt and Ann paused to personally reach out to extend us sympathy, and express their love," said the Massachusetts woman.

"It seems to me when it comes to loving our neighbour, we can talk about it, or we can live it. The Romneys live it every single day."

They were the types of stories that must have been regarded as a manna from heaven by prominent Republican politicians, pundits and strategists alike, all of whom had spent the day urging the Romney campaign to show Americans their candidate's human side.

A video segment featuring home movies of Romney cuddling and playing with his young boys also pulled at the heartstrings of delegates.

Romney, in his second bid for the party's nomination, spent much of the day tinkering with his speech, ensuring he got it just right. Long hesitant to delve into his faith -- a point of contention for some Christian evangelicals in the party's base -- Romney was reportedly determined not to shy away from his Mormonism at the convention.

A common practice in Mormon churches is to help church members move house and "to help each other out in different ways," Romney said.

"And that's how it is in America. We look to our communities, our faiths, our families for our joy, our support, in good times and bad. It is both how we live our lives and why we live our lives. The strength and power and goodness of America has always been based on the strength and power and goodness of our communities, our families, our faiths."

Romney's speech was preceded by a slew of marquee speakers on the convention's closing night -- including Hollywood movie star Clint Eastwood, who provided the weirdest moment of the convention as he assured the crowd not all actors are "lefter than Lenin."

"There are 23 million unemployed people in this country, and that is a disgrace," Eastwood said before thrilling the crowd with a bizarre pretend conversation with an invisible Obama.

"And I think possibly that now it may be time for somebody else to come along and solve the problem."

He ended by giving in to the crowd's demands to deliver his famous "Dirty Harry" line. Eastwood intoned: "Go ahead." The audience responded with glee: "Make my day."

American Idol star Taylor Hicks also performed on Thursday night, while Jeb Bush, Newt Gingrich and Sen. Marco Rubio spoke. Romney's youngest son, Craig, also addressed the convention in Spanish via video.

Romney bests Obama in public opinion polls on the economy, but the president consistently has a higher likeability rating. Romney's critics accuse him of being robotic and wooden on the campaign trail.

His likeability numbers, in fact, are among the lowest of any recent presidential challenger. A new ABC News/Washington Post poll, released Wednesday, suggested Romney is the least popular major-party nominee in more than 30 years.

But another public opinion survey released Thursday showed Romney is indeed benefiting from a bounce in the polls thanks to the convention.

Romney leads with 46 per cent support, compared to 42 for Obama, according to a Reuters-Ipsos national tracking poll.

The former Massachusetts governor struggled to connect with Republican voters during a fractious primary season -- eyed with suspicion, in particular, by the Christian evangelicals and social conservatives among the party's base who fear he's secretly a moderate on social issues.

There's plenty of time before the Nov. 6 election for Romney to change perceptions, said Mike DuHaime, a top adviser to New Jersey Gov. Chris Christie, whose self-promotional speech to the convention two days earlier raised eyebrows among delegates and pundits alike.

"Most regular voters are just tuning in now for the first time," DuHaime said. "What I hope is we'll now see who Gov. Romney really is. We already know he's competent, and can handle the job of being president."

Romney's moment of triumph at centre stage came after a passionate warm-up act from Ryan, his budget-slashing running mate, on Wednesday night. Ryan electrified delegates by taking repeated aim at Obama, mocking and ridiculing the president's policies and his "failed" message of hope and change.

Romney hammered away at that theme in his own speech, albeit with a more positive approach.

"To the majority of Americans who now believe that the future will not be better than the past, I can guarantee you this: if Barack Obama is re-elected, you will be right," he said.

"I am running for president to help create a better future. A future where everyone who wants a job can find one. Where no senior fears for the security of their retirement. An America where every parent knows that their child will get an education that leads them to a good job and a bright horizon."