TAMPA, Fla. — Through three nights of gauzy videos, sentimental testimonials and, finally, his own address to the nation Thursday, Mitt Romney worked hard to show he has a heart.  Mitt Romney said Americans had been patient with President Obama but could wait no longer for improvement.  But he still needs to tackle the much harder job of convincing those Americans who so emotionally invested their hearts in President Obama four years ago that it is time to accept that his presidency did not work, let go of him and move on.  Not even Mr. Romney’s own strategists are pretending that is going to be simple. And even before leaving the nominating convention here, they were beginning a delicate 10-week campaign aimed at those voters who are disappointed in Mr. Obama but just can’t yet bring themselves to quit him.  After month after month of disappointing job numbers, poll after poll showing dissatisfaction in his economic performance and hundreds of millions of dollars in negative advertisements, a large portion of wavering voters maintain a personal attachment to Mr. Obama, and a tentative willingness to give him more time to get it right, top strategists with both campaigns agree.  That is a testament, perhaps, to the power of that scene four years ago when Mr. Obama and his family crossed the threshold of the White House as its first African-American tenants, “an inspiring moment that so many have awaited so long” as former President George W. Bush — the man he was so hard on in 2008 — put it then.  Representative Paul D. Ryan may have painted a biting picture on Wednesday night when he referred to the faded Obama poster hanging above unemployed college graduates’ childhood beds, but the poster was still there, after all.  Most challengers face the relatively clinical task of persuading voters to fire the incumbent. Mr. Romney faces the more fraught mission of persuading them to break up with the incumbent.  “It’s going to be hard to break the bond a lot of voters feel with Obama, even if they are disappointed,” said Mark McKinnon, a former strategist for Mr. Bush. “It may be a bad marriage, but they still want to save it.”  It is Mr. Romney’s job now to convince them that it is beyond repair; that the risks of staying in it are larger than the risks of starting anew with him, that he and Mr. Ryan represent a fresh start akin to a generational change.  But leading these voters — many of them women — to that conclusion takes finesse and delicacy, Republican strategists say. The sort of visceral attacks that conservative talk show hosts are calling for risk sending them into a defense posture on behalf of Mr. Obama and, more to the point, of their own decisions four years ago.  Rather, strategists say, it requires providing a path that gives them permission to make a break. They need to be told that it is O.K. to remain proud of their initial support for Mr. Obama, but that they can be equally at peace with a decision to change their minds now.  “There is no need to make people feel bad about what they’ve done to feel good about what they’re going to do,” said Stuart Stevens, a senior adviser to Mr. Romney, as he sat in the empty convention hall Thursday afternoon in nervous anticipation of his boss’s speech.  So it was that Mr. Romney went out of his way to tip his hat to the historic import of Mr. Obama’s election, when he said “many Americans felt a fresh excitement about the possibilities of a new president.”  But, in what amounted to perhaps the most forceful and effective portion of his address, Mr. Romney sought to give Mr. Obama’s wavering 2008 voters a strong nudge from what he portrayed as a reverie, saying they have given the president time enough. “Americans have been patient; Americans have supported this president in good faith,” he said to a roar in the hall. “Today the time has come to turn the page.”  The exhortation seemed aimed at disappointed swing voters, who, some polls show, might be inclined to give Mr. Obama more time because he inherited an economy in dire shape.  Mr. Romney’s tone — more lament than anger — appeared to some analysts to be the most effective means of wresting away former Obama voters. “There are signs he is making progress,” Mr. McKinnon said, pointing to some polls that show Mr. Obama trailing Mr. Romney among independent voters.
The challenge for Mitt Romney may be that even Americans who are unhappy with President Obama remain personally attached to him.