Sen. Rand Paul (R-Ky.) found himself in hot water this week over his comments about child vaccination. (John Locher/AP)

Rand Paul’s plan to get himself elected president relies on two long-shot bets coming true.

So far, neither one seems to be going well.

Paul’s first wager is that his “libertarian-ish” ideas will manage to attract Republicans mad about regulation and Democrats mad about government spying — forming an entirely new American voting bloc. “The leave-me-alone coalition,” Paul calls it.

The second bet is a bet on Paul himself — a wager that he’s an unusually talented politician persuasive enough to build a coalition out of groups that have never viewed themselves as allies.

This week, Paul’s ideas put him at the middle of a national controversy when he applied his trademark libertarian, skeptical thinking to the question of childhood vaccines. They should be largely voluntary, Paul said, as a matter of freedom. He also said he had heard of children who “wound up with profound mental disorders after vaccines.”

At times, he has seemed uninterested in — or unprepared for — the basic tasks of being a national politician.

For instance, this week he “shushed” a female interviewer on national TV. After his vaccine comments drew angry reactions, he accused the media of misconstruing his remarks about vaccines and mental disorders.

“I did not say vaccines caused disorders, just that they were temporally related,” Paul said in a statement. “I did not allege causation.”

Paul could not be reached for comment for this article, and e-mails seeking comment from aides at his political action committee, RANDPAC, were not returned. A spokesman for Paul’s Senate office, when asked whether Paul could comment about his missteps this week, wrote back with a one-word message.

“Seriously?” spokesman Brian Darling wrote.

Seriously, he was told.

Darling did not reply after that.

Paul — the son of libertarian leader and three-time presidential candidate Ron Paul — has not formally said he’s running for president. But he’s showing all the symptoms. Rand Paul has hired top-flight GOP operatives, has visited New Hampshire and is planning a trip to Iowa this weekend.

Right now, polls put Paul near the top of a crowded and muddled GOP field.

National surveys have shown him running slightly behind former Florida governor Jeb Bush, with his support at roughly 10 percent among Republican-leaning voters. A recent poll in Iowa showed that 64 percent of likely caucus-goers had a favorable opinion of Paul. That was tied for second, behind former Arkansas governor Mike Huckabee.

That is better than Paul’s father was doing at the same point four years ago, but not by much.

He has said his candidacy will work if it catches the country at a fed-up, libertarian moment.

“I think there is a moment that has come to the country, where . . . the ‘leave-me-alone coalition,’ or the limited-government types, [are] the majority,” Paul told a gathering of young libertarians last year. “People aren’t really happy saying, ‘I’m a Republican’ or ‘a Democrat.’ There is a plurality of people, though, that are a little bit of both. . . . We can find that sweet spot, bring those people together.”

He would advocate both an old conservative value — “economic liberty,” the right to conduct business without government meddling — with an appeal to “personal liberty,” including traditionally liberal causes such as privacy protections and criminal justice reforms.

A year before the first caucus and 21 months before the general election, it’s impossible to know whether Paul’s libertarian moment will arrive at the right time. The state of the international battle against the Islamic State, for instance, could determine whether Paul’s skeptical views on war seem prescient or out of touch.

For Paul, then, it is vital to control the factors that lie within his grasp. In his speech to those young conservatives, Paul said it was important to project a hopeful, almost joyous attitude.

“Sugarcoat it with optimism,” he told the crowd, “like a man coming over the hill singing.”

This past week, Paul did not look like a man coming over the hill singing.

“Hey, Kelly! Hey, hey! Shhhhh!” Paul said to CNBC anchor Kelly Evans, putting his finger to his lips, when Evans interrupted him during an interview about a tax proposal. “Calm down a bit here, Kelly. Let me answer the question.”

On the subject of vaccines, Paul struggled with what might be the first rule of presidential campaigning: Try not to shoot yourself in the foot. And if you do, stop shooting.

First, he was asked about vaccinations on Laura Ingraham’s radio show. Paul said that he was not against vaccines but that “most of them ought to be voluntary.”

After that raised a controversy, Paul reacted first with sarcasm: “Well, I guess being for freedom would be really, uh, unusual?” he said on CNBC. “I guess I don’t understand the point.”

Then he tried spin, saying he hadn’t meant what he’d seemed to say about vaccines and mental disorders. Finally, he sought to play the victim. Paul posted a photo of himself getting a vaccine booster shot on Twitter, with a caption that included the line, “Wonder how the liberal media will misreport this?”

Paul’s handling of the vaccine issue is one of several instances recently in which he has seemed to struggle with the kind of high-pressure interactions that would become run-of-the-mill for a presidential candidate.

Last month, Paul spoke onstage — along with fellow senators and proto-candidates Ted Cruz (R-Tex.) and Marco Rubio (R-Fla.) — at a gathering of wealthy conservative donors in Rancho Mirage, Calif. Rubio wore a suit. Cruz wore a jacket and slacks. Paul, following a personal fashion trademark, wore blue jeans.

That was viewed by some in the room as inappropriately informal for an aspiring presidential candidate.

Paul also stuck out for his tone. He was low-key, almost weary, while the other two were polished and energetic.

The senator from Kentucky also found himself on the defensive when the discussion turned to topics such as normalizing relations with Cuba and negotiating with Iran. While Cruz and Rubio drew whoops and applause for hard-line stances denouncing the Obama administration’s approach, Paul’s arguments for diplomacy were met largely with quiet.

“He probably started the weekend with the highest burden of expectations, and he failed to meet them,” said one attendee, who spoke on the condition of anonymity to discuss the private event. “It wasn’t that he made significant mistakes. It’s just that he looked lackadaisical and to an extent even disinterested.”

Because he was on that stage in California, Paul wasn’t in Iowa, where a key gathering of conservatives was hosted by Rep. Steve King (R) on the same weekend.

There, some evangelical voters said they were already wary of Paul because of his attempt to appeal to both left and right. To evangelicals, Paul is trying to be on both sides of issues with only one right side.

Paul has said he opposes same-sex marriage, for instance. But he’s also said that the issue should be settled on a state-by-state basis. And he opposes abortion but has said that given public attitudes, U.S. law on the subject is not likely to change soon.

And now, Paul had again missed a chance to make his case to Iowa Republicans at an important conservative event.

“Dude, who do you think you are?” Steve Deace, a conservative activist who hosts a popular Christian radio talk show in Iowa, said of Paul. “You think you are so big that you can avoid the process, that you can just bypass all of the major events” on the Iowa conservative calendar?

“I don’t know where he is getting advice on this,” Deace said. “But right now he is going nowhere.”

If Paul runs for president, there will be more weeks like this one. Paul will have to get better at projecting competence and confidence in uncomfortable situations. If he doesn’t, his moment might never come.

“He obviously is a guy who’s only run one race for office. So we’ll have to see how good his own political skills are,” said David Boaz, an executive vice president at the libertarian Cato Institute. After this rocky week, Boaz added, the best consolation for Paul is that we all may forget this ever happened.

“We’re still a year away from anybody voting,” he said. “If you’re going to make stumbles, better to do it now than the month before Iowa.”

Tom Hamburger contributed to this report.