Another prominent Republican gathering, more evidence of the dueling legacies of President Ronald Reagan overhanging the party as it tries to widen its reach and avoid extending its presidential losing streak in 2016.

There's Reagan the doctrinaire icon of modern conservatism who declared at his inauguration that "government isn't the solution; government is the problem." Then there's Reagan the pragmatic president who negotiated with Democrats and other Republicans on taxes, spending and immigration, among other issues.

Both Reagans made an appearance at a national conservative summit in Louisiana, and the divide is at the core of the GOP's identity search that pits tea party conservatives like Texas Sen. Ted Cruz and Utah Sen. Mike Lee -- they led a budget fight that sparked a partial government shutdown last fall -- against party establishment figures who say compromise is a necessary function of government.

Cruz told Republican Leadership Conference delegates Saturday at the Republican Leadership Conference that Reagan was successful because he was unapologetically conservative.

"Y'all will remember what happened in 1980," Cruz said. "We saw ... millions of Americans across this country rise up and become the Reagan revolution."

Haley Barbour, the former Republican national chairman who worked in the Reagan White House, delivered a history lecture on the same stage as Cruz a day before. "Reagan compromised on everything," he said, adding that "purity is the enemy of victory" in politics and in governing.

Barbour cited overhauls of Social Security, taxes and immigration that Reagan signed after deals with a Democratic Congress. He didn't say it, but the Social Security deal raised payroll taxes on some workers. The immigration law included provisions many Republicans now deride as "amnesty." Other Reagan tax bills included various cuts and increases.

After leaving office, Reagan also urged Congress to adopt the Brady Bill, which eventually passed to require a waiting period for certain gun purchases and a ban on certain military-style rifles. The law was named for a Reagan aide shot in a 1981 assassination attempt on the new president.

Cruz said Saturday: "In Texas, we define gun control real simple. That's hittin' what you aim at."

The senator won the presidential straw poll at the three-day conference, an annual gathering where some White House hopefuls make their pitch to some of the party's most conservative activists. Delegates said they're intent on reclaiming the White House and recognize the necessity of reaching behind the party's most conservative core, but there's little consensus on how to do it.

Cruz told The Associated Press after his speech that Reagan "unequivocally" would have aligned with him last year when he pushed Republicans to block budget bills in an effort to repeal President Barack Obama's health care overhaul. He conceded that Reagan signed eight deficit-spending budgets he negotiated with liberals like House Speaker Tip O'Neill of Massachusetts.

But those deals, Cruz argued, still "slowed the rate of growth."

"The difference was he was at least fighting for it," Cruz said. "Too many Republicans start with surrender and then are surprised when they don't get anything."