Republican presidential candidate Sen. Ted Cruz of Texas steps up his outreach Friday during a campaign event at Iowa Lake Community College in Emmetsburg, Iowa. (Joshua Lott /for The Washington Post)

Ted Cruz did not act like a candidate who had just been pummeled in a Republican debate the night before. The Texas senator and tea party darling was instead focused on imploring a group of voters in this tiny northern Iowa town to come caucus for him in three days — and to get others to do the same.

“I want to ask everyone here to vote for me 10 times. Now, we’re not Democrats. I’m not suggesting voter fraud,” Cruz said Friday, standing in front of a popcorn machine at a bar as the crowd chuckled. “But if everyone here gets nine other people to show up Monday night, you will have voted 10 times. That is how we win.”

Cruz, not long ago leading GOP front-runner Donald Trump in the polls here, has had a rough couple of weeks — under siege from all sides, sliding back to second place and targeted Thursday night in a debate where much of the fire, and a good deal of the damage, was borne by him.

Now, with the first-in-the-nation Iowa caucuses set to be held Monday, Cruz is blitzing the state to get as many people as possible to vote for him. He is also focusing new attacks on another rival, Sen. Marco Rubio of Florida, including a fresh round of advertising to be aired this weekend.

Despite such headwinds, the Cruz campaign — modeling itself as a conservative version of President Obama’s ground operation — said Friday it remains serenely confident that two things will carry him across the finish line here: superior organization and analytics.

Cruz is locked in a tight battle with Trump, and the two have followed very different strategies. Cruz’s is the more traditional one, intensely focused on the ground game. Trump thinks that he can bring voters to the caucuses through the force of his celebrity and personality, which has drawn tens of thousands of supporters to his rallies.

Cruz’s campaign manager, Jeff Roe, laid out the challenge in pinpoint detail Friday at a breakfast in Des Moines organized by Bloomberg Politics.

The operation of the senator from Texas thinks that it has come down to fighting over exactly 9,131 voters who are trying to decide between Cruz and Trump: 3,185 who are torn between him and retired neurosurgeon Ben Carson; and a smaller group — 2,807, to be precise — who have not yet made their choice between him and Rubio. Cruz also must try to peel off supporters of other religious conservatives in the race, including former Arkansas governor Mike Huckabee and former senator Rick Santorum of Pennsylvania.

“It’s very primal, frankly,” Roe said, when asked how he could be so confident of that data. “It’s not like kernels in the jar at the state fair. These are people who have told us this. . . . The numbers aren’t wrong, because we’ve been testing them.”

Roe also predicted that turnout will exceed the record for a Republican caucus day, which is 122,000 in Iowa. What he doesn’t know, Roe said, is by how much. He conceded that the higher it goes, the better it will bode for Trump, who is counting on a surge of voters who have not traditionally made the effort to attend the caucuses, an exercise that requires devoting most of a frigid weeknight.

The Fix's Chris Cillizza previews the Iowa caucuses, looking at what the outcome could mean for both Democrats and Republicans. (Peter Stevenson/The Washington Post)

In the final days, he added, Cruz plans to stick to the message that has gotten him this far — the promise that he will be the ultimate disrupter of how Washington operates. But it will have one additional pitch.

“This is now a choice. In many respects, Mrs. Clinton’s problems have led Republicans to believe they are picking a president now,” Roe said, referring to the difficulties Democratic front-runner Hillary Clinton is having in her primary battle with Sen. Bernie Sanders of Vermont.

“Now, the question Republican primary voters are asking is, ‘Who do we want our president to be?’ Not just, ‘Who do we want our nominee to be?’ ” Cruz’s campaign manager said. “That’s a different calculation for people.”

In recent days, Cruz and his surrogates on the campaign trail and on television have been making that entreaty to voters, telling them that it is effectively a “two-man race” between him and Trump, and that Cruz is the only candidate with the conservative record, money and organization to beat the businessman. They say that Trump would support “Bernie Sanders-style” socialized medicine, was an abortion rights advocate for most of his life and supported a pathway to citizenship for undocumented immigrants. They highlight Trump’s decision to boycott Thursday night’s GOP debate in Des Moines, saying that it shows he does not have the “humility” to stand in front of Iowans with other candidates.

Cruz has also been talking up values on the campaign trail, as well as his desire to stop federal funding for Planned Parenthood and his antiabortion views. He asks voters whether they have ever been “burned” by a politician, and he promises that if he is elected they won’t be.

“So even if you’re thinking about another candidate, the simple reality is there is only one campaign that can beat Trump,” Cruz told a private meeting of pastors this week.

On the financial side, the campaign will officially announce Sunday that it had more than $19 million in its campaign coffers as of Dec. 31, which Roe said will be $10 million more than any other GOP presidential candidate can claim. Trump is in a different category, as he is funding a good portion of his campaign with his personal fortune.

Roe said that the figure is evidence Cruz is financially equipped to battle it out for what could be months left to go in the GOP primary race.

Beyond Iowa, Cruz’s campaign has focused resources on the delegate-rich South, which has a slate of states that vote March 1. Cruz has spent about a quarter of his time there, including about a dozen slickly produced rallies in December that had the feel of a general-election swing.

But Cruz must get through the Hawkeye State first. Cruz has promised to visit all 99 Iowa counties, a challenge he is set to complete Monday. But days before the caucuses, the pledge is taking him away from the state’s population centers to out-of-the-way places such as this town of about 400 people near the Minnesota border.

One of Cruz’s persistent problems here is his stance on ethanol, a big business in this agriculturally rich state. Cruz opposes a mandate that requires gasoline to have a certain percentage of the corn-based fuel, decrying it as corporate welfare that makes Washington lobbyists rich and hurts competition. He is asked about it at almost every campaign stop, telling voters that he supports ethanol but opposes Washington.

Iowa Gov. Terry Branstad (R) has taken the unusual step of publicly hammering Cruz on the issue, saying it should force him to lose the caucuses. Branstad said Friday that Cruz turned in a “poor performance” in the debate and is fading, in part because of his ethanol position.

“Renewable energy is very important to our state. A lot of jobs are at stake,” Branstad said in an interview on C-SPAN’s “Newsmakers.” “His stand on that issue is definitely going to hurt him.”

Here in Ringsted, Cruz was asked repeated questions about the issue by a woman who brought up Branstad; Cruz pointed out that the governor’s son is an ethanol lobbyist. Cruz said that he refuses to capitulate to those who said his stance on the issue will hurt him here.

“I understand it would be easier to come to Iowa and say, ‘I’m for the ethanol mandate forever and ever, Amen.’ I get that,” Cruz said.

But then he pivoted to another growing threat: Rubio, who has been shown gaining on Cruz and Trump in recent polling here. The focus of Cruz’s attacks on Rubio, both on the stump and in the new round of advertising, is Rubio’s co-sponsorship of a failed Senate immigration-reform bill that Rubio now disavows.

“Marco Rubio has gone on Univision in Spanish and said, ‘No, no, I won’t rescind amnesty,’ ” Cruz alleged in front of the Ringsted crowd.

In his recent Iowa appearances, Cruz emphasized that the only way to beat Trump or Rubio is to turn out to caucus.

“Call your mother. Call your sister, your next-door neighbor, your business partner,” he says, reminding people it’s always a good idea to call your mother.

He’s also making promises. At a community college in Emmetsburg, Iowa, on Friday, Cruz joked: “Everyone who comes out and caucuses gets two free library books.”

Tumulty reported from Des Moines.