Jeb Bush signs autographs after a town hall meeting Saturday at Loras College in Dubuque, Iowa. (Aaron P. Bernstein/Reuters)

To take back the White House after eight years in the political wilderness, Republicans think they must soften their image and expand their appeal in particular to women and Latino voters. As Jeb Bush, a leading presidential contender, puts it, “We’re going to win if we show our hearts.”

But the GOP’s strategic imperative is running headlong into its structural reality.

Party officials are growing worried about a wide-open nominating contest likely to feature a historically large and diverse field. At best, they say, the Republican primaries will be a lively showcase of political talent — especially compared with the relative coronation taking shape on the Democratic side. But officials also acknowledge just how risky their circumstance is for a party that hasn’t put on a good show in a long time.

With no clear front-runner and Bush so far unable to consolidate his path to the nomination — his fumbles over the Iraq war and his brother’s legacy further exposed his vulnerabilities — the GOP’s internecine battle could stretch well into the spring of 2016.

This could cost presidential aspirants tens of millions of dollars; pull them far to the right ideologically, from hot-button social issues to foreign policy; and jeopardize their general-election chances. And in such a muddled lineup — officials are planning to squeeze 10 or more contenders onto the debate stage — candidates will be rewarded for finding creative ways to gain notice.

Sen. Marco Rubio, R-Fla., addresses the Georgia Republican Convention on Friday in Athens, Ga. (David Goldman/AP)

“We’re in a danger zone,” said Doug Gross, a top Republican establishment figure in Iowa. “When the party poobahs put this process together, they thought they could telescope this to get us a nominee who could appeal to a broad cross-section of people. What we’ve got instead is a confederation of a lot of candidates who aren’t standing out — and in order to stand out, you need to scream the loudest.”

Looming above the GOP show is Hillary Rodham Clinton, the dominant Democratic candidate whom Republican officials brashly dismiss as a scandal-plagued, out-of-touch relic of the past but whose early strength and political durability is nevertheless giving them a serious scare.

Republican officials are dismayed that months of relentless, negative press coverage of her use of private e-mail servers, foreign donations to her family’s charitable foundation and her six-figure paid speeches have done minimal damage to her favorability ratings.

At last week’s Republican National Committee meeting in Scottsdale, Ariz., party leaders plotted their path back to power and confronted the demographic changes that have made the Electoral College more challenging for Republicans, with their heavily male, overwhelmingly white base.

“To win in a presidential election year, the Democrats have to be good,” RNC Chairman Reince Priebus said. “As Republicans, we need to be about perfect in order to win.”

Perfection will be difficult to achieve, however. At the start of the year Bush was seen as the most electable contender and a favorite for the nomination. Thanks to his dynastic family’s deep network, Bush began building a juggernaut of a campaign.

But he has shown himself to be politically rusty, most acutely last week, as he twisted himself into knots over the unpopular war started by his brother, former president George W. Bush. Finally, he said on Thursday that he would not have invaded Iraq had he known about the intelligence failures at the time. Meanwhile, among activists in the early voting states, the former Florida governor has yet to catch on, raising doubts about his ability to unite the party.

Wisconsin Gov. Scott Walker arrives for the Chad Airhart Blue Jean Bash fundraiser on Saturday in West Des Moines, Iowa. (Daniel Acker/Bloomberg)

Instead of a front-runner, Republicans have an array of candidates demonstrating strength. Wisconsin Gov. Scott Walker got off to a fast start in January and sits at or near the top in many polls, while Sen. Marco Rubio (Fla.) rose with a splashy April campaign launch that highlighted his charisma and youthful vigor. Others have impressed, too, including Carly Fiorina, a former technology executive and the lone woman in the field, who is considered a long shot but wowed RNC members in Scottsdale with her substantive stump speech and cutting attacks on Clinton.

Republican activists love that they have so many candidates to consider. At Bush’s event, Darlene Block, 73, the party co-chairman in Jackson County, ticked through her short list: “Jeb’s on it. So is Dr. [Ben] Carson. And I like — I keep forgetting his name, but he’s the senator from Florida. Marco? Marco Rubio! I’m terrible on names. I’ve met Ted Cruz, I’ve found that [former Texas governor Rick] Perry was so much more sensible than I thought he would be. . . . And Rev. [Mike] Huckabee. . . . They all are so good.”

Party officials laud their deep field, drawing comparisons to the lengthy 2008 primary battle between Clinton and President Obama that ultimately worked to the Democrats’ benefit.

This time, argued Sean Spicer, the RNC’s chief strategist, “The attention’s going to be on our side, the horsepower’s going to be on our side, the enthusiasm’s going to be on our side.”

The downside is that with such stiff competition, there are incentives for candidates to make flashy moves that might stir the conservative base but turn off mainstream voters.

“If we go back to the old way of fighting amongst ourselves and saying, ‘You’re not righteous enough, you’re not perfect enough, you’re not this enough,’ we’re not going to win,” Bush said in a speech to RNC members this week.

This is particularly worrisome, considering the GOP is trying to shed its image as a retro party that protects the wealthy and project a more forward-looking vision by trying to demonstrate that Republicans care about the poor and disadvantaged and craft policies to lift them up.

“Anybody who doesn’t believe this hasn’t been paying attention the last few years,” said Matt Borges, the party chairman in Ohio, the quintessential general election swing state. “If our party isn’t seen as leading on these things, we’re running the risk of becoming a permanent minority.”

Borges said he sees only a few contenders developing that message: Bush, Rubio, Ohio Gov. John Kasich and former Pennsylvania senator Rick Santorum.

Borges and other prominent Republicans said they fear if the primary campaign devolves into a purity test — or “a theology class,” as former Oklahoma governor Frank Keating put it — there could be trouble.

“To have a baker’s dozen and a few more as our candidates is impressive, enabling and exciting,” Keating said. “But it’s problematical, because if it looks like total chaos, people will switch the channel.”

For now, the candidates say they want to avoid chaos.

“This whole process is to elect a Republican nominee,” Huckabee, a former Arkansas governor, told reporters Friday in Scottsdale. “It’s not to provide a media circus. It’s not to provide entertainment to the masses and to create a show that would be delightfully pleasant for the opposition to watch.”

But they may not keep their word. “You always hope that we follow what Ronald Reagan said about not criticizing each other, but that’s probably not the real world,” said Rob Gleason, chairman of the Pennsylvania Republican Party.

Last week brought a preview of the jousting to come. As Bush struggled to talk about Iraq, many of his GOP rivals pounced to make unfavorable correlations between him and his brother, who left office with dismal approval ratings. “There’s plenty of time for the Bush comparisons,” Santorum said, while Sen. Rand Paul (Ky.) warned the country could get “George Bush 3.”

“I think, without question, the toppling of [Saddam] Hussein made the place less stable, more chaotic, more of the rise of radical Islam, more of the ascendance of Iran, and did no good for America,” Paul said Saturday in Iowa. “We should’ve never gone in.”

Campaigning in Iowa City, Bush was asked Saturday why he wasn’t better prepared for questions about Iraq and whether his fumbles are a sign of weakness.

“Nah, I don’t think so,” he told reporters. “Look, we are all going to make mistakes. If you’re looking for a perfect candidate, he probably existed 2,000 years ago.”