Tampa – It’s the oldest political rap against Mitt Romney: He is an ideological weathervane, a politician with a well-deserved reputation for conveniently reversing past positions. His history of ideological reinvention – from a self-described moderate whose “views are progressive” to a “severely conservative” Republican – has been explored, attacked, defended, and ridiculed ever since he began testing the presidential waters eight years ago. Like his business acumen, his storybook marriage, and his Mormonism, Romney’s political switchbacks have become a mainstay of his public image.

The former Massachusetts governor will give one of the biggest speeches of his political career at the Republican convention here tomorrow night. An essential goal of the speech is to reboot that public image. Party conventions are no longer just about rallying the faithful. More important is making a good impression on the “persuadables,” the narrow slice of the electorate that is still undecided about whom to vote for, or at least open to a convincing argument to change their minds.

Romney’s nationally televised acceptance speech may be his best chance before November to assure ambivalent voters that his core beliefs are not apt to shift with the prevailing breezes. With Hurricane Isaac’s capricious winds and unpredictable trajectory, there has been no shortage here of meteorological metaphors for expressing the virtue of political dependability.

But a counter-theme pulsing through this GOP convention week is that there are times when people should reverse themselves on significant political issues. If you were convinced in 2008 that putting Barack Obama in the White House was of surpassing importance, Republicans in Tampa want you to know: It’s OK to change your mind.

Hence the speaking slot last night for Artur Davis, a former Democratic congressman from Alabama. In 2007 Davis was one of the first public officials outside Illinois to endorse Obama’s presidential bid. At the Democratic convention the following year, he was chosen to second Obama’s nomination. What appealed to him was Obama’s rhetoric of moderation – his promise to rise above Red-Blue divisiveness and bring the country together.

“I really believed that Barack Obama’s election would permanently change America for the better,” Davis told me this week. “I thought he would reduce the polarization of our political debate. Instead we’re more polarized than ever.”

Disenchanted with his party’s forced-march leftward under Obama, Davis finally switched his registration to Republican. “The Democratic Party used to be open to many points of view,” he recalled. “That is no longer the case.”

Davis’s change of heart is striking, but skeptics may be inclined to assume that anything said by a once-and-perhaps-future politician must be tainted by some ulterior motive. No one will feel that way about the people they meet in “The Hope and the Change,” a one-hour film produced by Citizens United and screened publicly for the first time in Tampa yesterday.

The film showcases 40 registered Democrats and independents, each of whom voted for Obama in 2008 and now is filled with buyer’s remorse. Many describe the deep joy they felt when Obama won. “I was actually happy to go to the polls; I was excited to vote for Barack Obama,” one woman says. “My heart was pounding, and I was like: Yes!”

But the euphoria faded, and, one by one, the Obama voters of 2008 explain how the president they elected so rapturously lost their support. For some it was the explosion of government debt, for others the massive “stimulus” that accomplished little. A common refrain is that the president seems to be in over his head, and way too eager for the trappings of celebrity. Many lament that the candidate who promised to be the nation’s great healer has increased the level of rancor poisoning American life.

What comes through most clearly, however, is the empty feeling of disappointment: “I voted for a change,” says a Pittsburgh voter, “but really – nothing happened.”

Heading into a breakfast here yesterday morning, former Massachusetts Governor Bill Weld acknowledged that he too has had buyer’s remorse. “I was part of the army that thought he was going to be absolutely fabulous,” said Weld, who made news in 2008 when he crossed party lines to endorse the Democratic nominee. But Weld isn’t re-enlisting this time around.

Obama’s army isn’t nearly the mighty force it was four years ago. Persuading even more Americans that it’s OK to have changed their minds about the president is Romney’s foremost mission this week. That, and reassuring them that his own political fidelity will be rock-solid.

(Jeff Jacoby is a columnist for The Boston Globe. His website is www.JeffJacoby.com).