The one-two finish of Rand Paul and Ted Cruz in The Washington Times/CPAC straw poll over the weekend cemented their rock star status among grass-roots activists — and signaled that the two tea party favorites are destined for a showdown over which senator will carry the conservative flag in the contest for the 2016 GOP presidential nomination.

For the second straight year, Mr. Paul was easily the top choice of the thousands who converged for the three-day Conservative Political Action Conference just outside the Beltway in suburban Maryland, underscoring the power of the libertarian wing of the movement.

Mr. Cruz, meanwhile, showed that his star is on the rise among this pool of conservatives, as he climbed up the standings from a year ago to finish a distant second.

“They are definitely on a collision course,” said Drew Ryun, political director of the Madison Project, which is supporting insurgent candidates against incumbent Republicans in primaries across the country. “It remains to be seen who gets the upper hand in this one, but make no doubt, it is between the two of them for the conservative movement when it comes to 2016.”

Mr. Paul took 31 percent of the nearly 2,500 votes cast, giving him an easy victory and building on his first-place showing last year.

Mr. Cruz jumped from 4 percent last year to 11 percent this year — good enough for second in a field with more than two dozen names.

“He is building a movement, and he is the most articulate,” said David Fitzwilliam, 83, of the District of Columbia.

Rounding out the top four were neurosurgeon Ben Carson in third place and New Jersey Gov. Chris Christie in fourth.

Mr. Cruz and Mr. Paul won primary challenges against establishment-backed Republican candidates — Mr. Cruz in Texas in 2012 and Mr. Paul in Kentucky in 2010.

Both men also have gained national prominence by leading old-style, hold-the-floor, talk-till-you-drop filibusters to highlight their chief issues. Mr. Paul drew attention to drones and their potential to invade privacy. Mr. Cruz’s talkathon was aimed at highlighting government spending and Obamacare.

Mr. Cruz’s style has agitated some of his colleagues, but Mr. Paul has been praised by Republicans and Democrats for his approach to both fighting and collaborating where he can on issues such as sentencing reform.

Mr. Paul also has worked to broaden the image of the Republican Party by arguing that minorities can be attracted to a libertarian message.

Despite their differences, both men are likely competing for the same voters, judging by the reaction at CPAC.

“My dream ticket would be Cruz and Paul,” said Jinny Walz, 73, of Kansas. “I think they are the ones who are the standard bearers for the conservative movement.”

Addressing CPAC Thursday, Mr. Cruz said the GOP loses when it waters down and moderates its messages, pointing to the failed presidential bids of Sen. Bob Dole in 1996, Sen. John McCain in 2008 and former Massachusetts Gov. Mitt Romney in 2012.

“They’re decent men,” he said. “But when you don’t stand and draw a clear distinction, when you don’t stand for principle, Democrats celebrate.”

Speaking Friday, Mr. Paul called on the crowd to elect “lovers of liberty” — not Republicans — who will join him in repelling the Obama administration, which he said is running roughshod over Americans’ civil liberties.

“We will challenge you in the courts. We will battle you at the ballot box. Mr. President, we will not let you shred our Constitution,” Mr. Paul said.

Mr. Paul’s CPAC supporters collected “Stand with Rand” stickers, posters and T-shirts.

“He is the only true liberty candidate who focuses on civil liberties more than anybody else,” said Al Seltzinger, 36, from Baltimore. “I think the way the nation is going today with the government and the president going against the Constitution that we need someone who holds strict to the Constitution and whose voting record is pretty solid when it comes to the Constitution.”

Michael Garcia, a 23-year-old student at Plymouth State University in New Hampshire, said Mr. Paul’s libertarian-infused conservatism resonates with young voters.

“We have grown up under surveillance between cameras on the streets, cellphones, the NSA,” he said. “We like how Rand Paul really fights against the surveillance, where we feel like we are always being watched and we feel like he protects our personal privacy.”

Mr. Cruz, meanwhile, placed first — and Mr. Paul a distant second — in an online poll from the Senate Conservative Fund. Mr. Cruz also was showered with praise by former Alaska Gov. Sarah Palin, the party’s 2008 vice presidential nominee and CPAC’s keynote speaker.

“Thank you, Texas, because liberty needs a Congress on Cruz control,” Mrs. Palin said to applause from the audience, some of whom wore “Cruz Crew” stickers.

There are signs, though, that the relationship between Mr. Cruz and Mr. Paul could be fraying and that tension could be growing as they approach the presidential nomination race, which kicks off in Iowa in about 22 months.

“I’m a big fan of Rand Paul; he and I are good friends. I don’t agree with him on foreign policy,” Mr. Cruz said Sunday on ABC’s “This Week.” “I think U.S. leadership is critical in the world, and I agree with him that we should be very reluctant to deploy military force abroad, but I think there is a vital role, just as Ronald Reagan did.”

Mr. Paul, meanwhile, took a swipe at Mr. Cruz on “Fox News Sunday,” suggesting that the Texas Republican’s no-holds-barred political style contrasts with attempts to broaden the party’s appeal.

“Everybody has their own style,” Mr. Paul said. “I don’t spend a lot of time trying to drag people down,” Mr. Paul said. “I don’t spend any time sort of trying to criticize others in the party because I realize the party has to be bigger, not smaller.”

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