By Gabriel Debenedetti

MANCHESTER, New Hampshire (Reuters) - Conservative Republican Senators Rand Paul and Ted Cruz tested the 2016 presidential waters at an event on Saturday in the influential state of New Hampshire at which potential opponents from the more moderate wing of the party did not appear.

The "Freedom Summit" rally was the latest in a series of stops for Cruz and Paul, who are hoping to win the favor of the party's right wing for potential White House bids.

The event was co-hosted by Americans for Prosperity, a group funded by the conservative billionaire Koch brothers and the single largest advertiser in the 2014 election cycle so far. Among other speakers was former Arkansas Governor Mike Huckabee, who ran for the Republican nomination in 2008 and is seen as a potential 2016 contender.

Paul, a favorite among libertarians, cautioned Republicans against compromising.

"Some say we just need to dilute our message, let's just be a little more like the Democrats," the Kentucky Republican told the audience. "You think that's a good idea? Hogwash. It's exactly the wrong thing to do. Our problem isn't that we are too bold. Our problem is that we are too timid."

Among the leading moderate Republicans, New Jersey Governor Chris Christie's 2016 prospects have been clouded by the "Bridgegate" traffic scandal, while former Florida Governor Jeb Bush appears in no hurry to join the race for the White House.

That has created an opportunity for others to try to make inroads in New Hampshire, the first-in-the-nation presidential primary state, where White House candidates often preview their campaign messages.

"You want to know why people are frustrated out of their mind in Washington? The biggest divide we have is not between Democrats and Republicans," Cruz, a Texas Republican, said at the event. "It's between entrenched politicians in both parties, and the American people."

While no politician has yet thrown a hat into the presidential ring, Cruz and Paul have been preparing for possible campaigns for months, undaunted by the Republican Party's reluctance to nominate a conservative in recent presidential elections.

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Over the weekend, Cruz headlined two rallies for activists and voters with the New Hampshire Republican Party. Paul appeared at two fundraisers with the state party and one for a non-profit group that has funded ads against the re-election bid of the state's Democratic senator, Jeanne Shaheen.

NO REAL FRONT-RUNNER

The fractured Republican field has no true front-runner 21 months before the first primary votes of 2016, unlike among Democrats, where former U.S. Secretary of State Hillary Clinton holds a large lead over other possible contenders.

The RealClearPolitics average of national polls taken from March 6 to 30 showed no potential Republican candidate with more than 15 percent support.

Paul, Cruz, Bush, Christie, Huckabee and Wisconsin Representative Paul Ryan each averaged between 8 and 15 percent in the RealClearPolitics sample. Polls this far ahead of elections are rarely predictive, and national appeal does not necessarily translate to primary-state popularity.

Cruz, a favorite of the conservative Tea Party movement, who has feuded with more moderate Senate colleagues, and Paul, whose libertarian leanings and non-interventionist foreign policy worry traditionalist Republicans, would have to broaden their appeal within the party to win the nomination, analysts said.

"There are not enough Tea Party people, not enough libertarian people, not enough socially conservative people to win a Republican nomination, by definition," said veteran Republican pollster Whit Ayres, who runs polling for Florida Senator Marco Rubio, another possible 2016 hopeful.

"Anyone who comes from one of those traditions must expand beyond that tradition to win," Ayres said.

A leading Republican critic of National Security Agency surveillance, Paul has appeared before a wide range of audiences, looking to woo social conservatives and young people. In March, he even spoke at the University of California at Berkeley, long known as a liberal stronghold.

"Anybody got a cellphone? You're under surveillance," he said on Saturday, holding one up. "Here's the thing: It's none of their damn business what you do with your cellphone."

In office less than two years, Cruz has been a frequent presence in early candidate-selection states like Iowa and South Carolina, and has rebounded from criticism from fellow Republicans over his role in the government shutdown last October.

The White House agreed on Friday with Cruz's call to deny a visa to Iran's choice for U.N. ambassador because of the envoy's suspected participation in a Muslim student group that seized the U.S. Embassy in Tehran in 1979 and held 52 Americans hostage for 444 days.

Bush and Christie did join other potential Republican candidates at a Las Vegas meeting in March with donor Sheldon Adelson, who spent more than $100 million in the 2012 election cycle.

Bush, who says he will decide whether to run by the end of 2014, ran into trouble with conservatives this week after characterizing illegal immigration as an "act of love" by those who come to the United States to provide for their families.

The first mention of Bush's name and his immigration comments drew boos from the conservative crowd on Saturday.

(Editing by Alistair Bell and Peter Cooney)