Sen. Rand Paul (R-Ky.) holds up his cellphone as he speaks in Louisville at the April kickoff of his presidential campaign. (Carolyn Kaster/AP)

Rand Paul notched a big victory in Washington on Sunday night by following through on his promise to block the renewal of the anti-terrorism law used to justify domestic spying programs.

But back in Iowa, where Paul has tried to use the issue in recent days to revive his struggling presidential campaign, many Republican voters have responded with unease.

Even some who stood in line to see Paul as he traveled the state last week said that they simply could not agree with his argument that the National Security Agency’s bulk data collection was an unreasonable invasion of privacy.

“If you’re not doing anything wrong, what are you worried about?” said Tom Charlton, 64, a retired sales training manager for a tire company, who was first in line at a book-signing with Paul in Davenport. “If this can stop one attack, it’s worth infringing on legal citizens’ rights.”

Vivian Martin, 71, bought a copy of Paul’s new book, “Taking a Stand,” and watched him speak here, but she said his views give her pause.

On the night the Patriot Act expired, Sen. Rand Paul (R-Ky.) equated the collecting of Americans' phone records to "what we fought the revolution over." (Senator Rand Paul/YouTube)

“I don’t want the mall to get bombed because they didn’t get the information they needed,” said Martin, who runs a water-softening business with her husband.

Another Republican, retired preschool teacher Sally Cram, 62, said after leaving a town hall meeting with Sen. Charles E. Grassley (R-Iowa) that she supports the NSA program because “I’m a person who believes our government tells us the truth.”

Paul’s anti-NSA crusade, culminating with Sunday’s Senate showdown, has differentiated him from a crowded pack of presidential candidates and re­invigorated the devoted activists and donors who zealously backed his father, Ron Paul, in 2012 and are crucial to the younger Paul’s chances.

But, as the skeptical response here has demonstrated, preaching to the choir is not necessarily winning over fresh converts. Paul’s hard-line stance on the NSA has found little resonance among the rank-and-file Republicans that he will need to win over if he hopes to find success in the caucuses here that kick off the presidential nominating calendar in February.

The dynamic suggests that Paul, whose campaign has stumbled since its launch in April, continues to struggle with competing political demands. On one hand, he must broaden his appeal in a party still largely defined by national security hawkishness — as evidenced by his softening views on foreign aid and military intervention. Yet he also must excite a core libertarian base, motivated by anger over the NSA and skeptical of interventionist foreign policy, which forms the backbone of the grass-roots network that has made Paul’s candidacy viable.

A new Bloomberg News-Des Moines Register poll shows that Paul is the first choice of 10 percent of likely Iowa GOP caucus-goers. That’s high enough for Paul to be tied for second place (behind Wisconsin Gov. Scott Walker), but the results reveal weaknesses. His standing, for instance, is well below the 21 percent tally won by his father in the 2012 caucuses. And the new survey found that Paul’s favorability rating has slipped by nine points since January, the biggest drop for anyone in the field.

The Sunday night deadline for reauthorization of the USA Patriot Act presented an opportunity — and Paul seized it with gusto.

He gave a filibuster-like speech of almost 11 hours on the Senate floor two weeks ago and blocked a temporary extension, bringing an early end to Congress’s Memorial Day recess and forcing the rare Sunday session. He vowed to delay an up-or-down vote on a compromise bill, called the USA Freedom Act, which overwhelmingly passed the House and has the support of a bipartisan coalition from President Obama to Texas Sen. Ted Cruz, a presidential primary rival.

In Iowa last week, as Paul greeted voters and book buyers, he pointed frequently back to the looming showdown in Washington to present himself as a champion of Americans’ constitutional rights.

Speaking at a minor-league baseball stadium on the Mississippi River, Paul opened by apologizing that his voice was “still a little raspy” because of his Senate talk-athon “to protect your privacy.” He received some loud cheers, but not everyone applauded.

Here in Davenport, he reached back to the American Revolution, comparing the Obama administration’s bulk data collection to the “writs of assistance” that were issued by the British.

“This is what John Adams said we fought the revolution over,” Paul said. “Yet I have trouble telling what the difference is between a writ of assistance, a generalized warrant and a warrant that’s today being issued by President Obama that says ‘Verizon’ on it.” He said that the data being gathered “is the very definition of a general warrant and something that we should rise up and resist.”

Paul allies say that the issue is a political winner because those who agree with the senator are passionate and will be energized to volunteer and turn out to vote — even though those who support the Patriot Act are less moved by the issue.

Even if Paul’s latest Senate maneuvers spark skepticism from many in his party, his team says that the issue can reassure those who backed his father but worry that he has sold out by cozying up to the GOP establishment.

The Paul team also argues that the issue could expand the electorate by galvanizing millennials to participate in the low-turnout Republican caucuses for the first time. The senator himself notes in his stump speech that recent surveys show that younger people are more likely to feel that government surveillance has gone too far.

In fact, polling is all over the place on the NSA issue, and opinions depend largely on how the question is asked. A New York Times poll in September found that 44 percent of Republicans thought that the government had achieved about the right balance in restricting people’s civil liberties to fight terrorism. About a quarter said that it did not go far enough, and a similar number said that it went too far.

Paul spokesman Sergio Gor said that the showdown is about principle, not politics. “Senator Paul will follow the Constitution over any poll,” he said.

Paul allies acknowledge that there has been a pendulum swing since 2013, when former CIA contractor Edward Snowden leaked details of the NSA programs and many conservatives responded with fury.

“It became a big deal after Edward Snowden, but now it hasn’t been in the news that much,” said Brian Duffy, 28, an executive at his family’s security business who was inspired to become a libertarian by Ron Paul but hasn’t yet committed to Rand Paul for 2016. “Unfortunately, people have come to accept that’s just how it has to be. Personally, I believe it’s a big encroachment on our privacy.”

For the most part, the issue comes up only rarely on the campaign trail in Iowa, even as Congress has been gripped by the reauthorization fight.

Grassley, who as chairman of the Judiciary Committee holds sway over the issue, said that basically nobody here had asked about it during his recent spate of town-hall meetings across the state.

At an hour-long meeting Thursday morning in the drab basement of a county courthouse in the small town of Tipton, Grassley fielded questions on immigration and Israel, entitlements and tax extenders, abortion and food stamps, the sequester and rural broadband — but there was nothing about the NSA.

Similarly, when Paul headlined a fundraiser for Grassley at a Davenport country club, the two senators answered questions from donors about taxes and the highway bill — but neither brought up their differences over the Patriot Act, and no one asked about it.

Grassley said in an interview that the issue has largely faded from voters’ minds.

“We haven’t had a terrorist attack,” he said. “That’s the difference.”

The issue also did not come up at campaign stops last week by former senator Rick Santorum (R-Pa.), who said he continues to support surveillance programs.

“This act’s been around for a long time, and it’s not like there are stories about horrible things that have happened to people,” Santorum said as he left the Machine Shed restaurant. “I don’t like bulk collection, but the Patriot Act has worked and we have to realize we’re at war.”

NSA officials say that the programs collect only metadata, such as phone numbers dialed and the duration of calls. Officials argue that this allows them to learn about a suspected terrorist’s affiliates without having to get individual search warrants.

Even so, a number of voters interviewed said they thought that the NSA records all of their phone calls and reads their ­e-mails. And, most of these voters said, that is fine with them.

“It doesn’t bother me because anybody who says illegal stuff on the phone is flat stupid,” Navy veteran Alan Loomis, 62, said after Santorum’s event. “I got my makeup and my smile on all the time because 90 percent of the places I go, I know I’m on camera . . . I just accept it. I don’t like it, but it’s part of the world now.”