The worst-kept secret in all-important Iowa is this: Rand Paul is running for president.

Journeying this week on a 10-stop, 800-mile tour of the state that holds the nation’s first presidential caucuses, the Republican senator from Kentucky has been bold not just in his rhetoric, but in his candor about preparing for a White House bid.

Paul is out-organizing his would-be 2016 rivals, building a network of loyalists in Iowa and other early-voting states while others lag behind and visit less often. He also sounds like a candidate, spitting out lines attacking Hillary Rodham Clinton, the potential Democratic nominee. He labeled the conflict in Libya “Hillary’s war,” and said the former secretary of state’s handling of the 2012 terrorist attacks in Benghazi, Libya, should preclude her from becoming commander in chief.

Paul, 51, an ophthalmologist-turned-tea party hero, offered himself to Iowans as a Republican standard-bearer who could broaden the party’s appeal to a diversifying electorate. “We should be bigger, bolder and better,” he said at each stop — without being “wishy-washy” or “Democrat-lite.”

But his vision of GOP outreach and inclusion clashed awkwardly with the party’s reality Monday night at a lakeside tiki bar here in rural Okoboji, where Rep. Steve King (R-Iowa) held a campaign fundraiser.

YouTube video by Matt Hildreth of immigration reform advocacy group America's voice shows Rep. Steve King (R-Iowa) at a fundraiser. Sen. Rand Paul (R-Ky.) was also in attendance and can be seen leaving the vicinity of the conversation. (Matt Hildreth via YouTube)

Paul was eating dinner at a small table with King when a self-described “Dreamer” immigration activist introduced herself to them. Paul made a hasty exit — he left his half-eaten hamburger on his plate and was visibly chewing as he stood up — as Erika Andiola, the activist, questioned King about his opposition to immigration reform.

King told her, “You’re very good at English,” to which she appeared to take offense. Minutes earlier, the congressman had talked in his speech about a recent trip to the border in Texas: “I planted a flag right out there on the river across from the Mexicans!”

Paul, after extricating himself from the situation, talked with a handful of reporters about 10 feet away.

The moment underscored the difficulty that Paul and any other Republican presidential aspirant will face in building a diverse national coalition to win a general election, while also incorporating the party’s more extreme elements.

The senator’s rhetorical approach to the border crisis was to blame President Obama and focus on his vows to take executive action. “I frankly do think we could do some kind of reform, but you can’t do it by royal edict,” Paul told Republicans at a midterm organizing event in Council Bluffs. “You can’t have a king doing it.”

Paul came to Iowa to build relationships with key activists and test his message as he moves toward deciding about a presidential campaign early next year. It is Paul’s 10th visit to Iowa in two years.

“I don’t know why Iowa keeps popping up on my calendar, but it seems to be pretty frequent,” he told reporters — a typical wink-wink comment suggesting that his candidacy is all but certain.

In an interview, Paul previewed how he would go after Clinton in a general election if he got the chance. He said her summer book tour has shown “how disconnected she is from the middle class.”

“To make a comment about how woeful her finances were when she’s worth supposedly between $100 million and $200 million — most of us, myself included, can’t imagine that much money,” he said.

Paul brought up the Benghazi attacks, saying he thinks Clinton did not pay enough attention to diplomatic security needs in Libya.

“We want the most competent and wise of humans to be in charge of our military,” he said in the interview. “She made a big deal about the 3 a.m. moment with Barack Obama, that she would be the one to be able to handle the 3 a.m. call, but they were calling her repeatedly for six months and she wasn’t even picking up the phone.”

Paul went on to blame broader upheaval in Libya on Clinton’s policies, saying: “There are some who call Libya ‘Hillary’s war.’ She was all for it. . . . And if you look objectively at Libya now, it’s a jihadist wonderland there.”

A Clinton spokesman did not return a request for comment.

In his speeches across Iowa, Paul repeatedly attacked Clinton and tried to connect her to the Obama administration, drawing hearty applause from his crowds of Republican partisans.

“It’s sort of like the ‘Old MacDonald’ song — here a scandal, there a scandal, everywhere a scandal,” he said in Okoboji.

But Paul largely avoided talking about foreign policy in his speeches. His anti-interventionist views have been the subject of considerable debate among Republicans in Washington. Texas Gov. Rick Perry, a potential 2016 GOP primary opponent, has said Paul’s worldview would “endanger our national security.”

Some Iowans said they were intrigued by the senator’s potential candidacy, but questioned whether he is commander-in-chief material.

“There are a lot of things I don’t know about Rand Paul, like his foreign policy,” said Dan Dennis, 52, a business owner in Marion who described himself as a libertarian. “Right now, our foreign policy is so in the toilet we’ll need somebody strong in that area.”

In a state that prizes retail politics, Paul cut a reticent figure on the stump. He often seemed introverted and averse to the kind of glad-handing and back-slapping that is a favorite pastime of some of his potential opponents. But his oddities also help underscore the outsider, anti-Washington posture that many GOP voters find appealing.

On Monday, Paul began the day wearing a necktie featuring dozens of miniature profiles of former president James Madison, known as the father of the Constitution. Arriving in Okoboji’s kitschy Barefoot Bar, he changed into a rainbow-striped dress shirt.

“My staff’s like, ‘You’re wearing that?’ ” Paul told his supporters. “I’m like, ‘Well . . . this is my choice. Live with it. . . . This is the best party shirt I’ve got.’ ”

Republican strategists here said they are impressed with Paul’s organizing. He is working diligently to maintain the libertarian-leaning network of his father, former congressman Ron Paul (Tex.), who ran for president in 2008 and 2012, while also reaching out to evangelical Christians, fiscal conservatives and moderates. Two top Iowa operatives, Steve Grubbs and A.J. Spiker, are working with him.

“He’s playing it smart,” said Tim Albrecht, a strategist who has worked for Iowa Gov. Terry Branstad (R) and former Republican presidential nominee Mitt Romney. “There’s a case for him winning the Iowa caucuses. He’s definitely the front-runner now.”

Nationally, too, Paul has an early organizational edge.

“There are other people running for president, but they’re not organizing the way he is,” said Spencer Zwick, who was Romney’s national finance chairman. “I think some would regret that because they’re going to find themselves not organized and not prepared to run a full-scale primary campaign.”

When Paul stopped by a GOP office in Council Bluffs to help boost local candidates, Justin Levins, 37, came up to greet the senator.

“Your filibuster last year was so exciting I went out and put on a [bumper] sticker, ‘I Stand with Rand,’ and I drove that car like 100,000 miles,” Levins said.

“I appreciate that,” Paul said, quickly turning to meet someone else.