Former Florida Governor Jeb Bush speaks at a Horry County Republican Party breakfast at Rioz Brazilian Steakhouse in Myrtle Beach, South Carolina, March 18, 2015. [Photo/Agencies]

Distancing himself from the pair, without being disloyal to his family, will be tricky for the younger Bush. His campaign logo "Jeb!" avoids using the family surname.

"I think the biggest hurdle is he is going to have to sell himself as his own person, not his brother and not his father," said Fran Hancock, 64, from Palm Beach, a supporter at the event on Monday.

Bush's speech was briefly interrupted by pro-immigration reform protesters and he responded: "The next president will pass meaningful immigration reform."

Bush held an early lead in opinion polls of Republican voters when he first began talking about a White House run six months ago, but that has now dissipated. He is essentially tied for the lead with a host of challengers.

Failure to deal with the Bush family legacy has already caused problems for Jeb, who fumbled a response last month to a question about whether he would have invaded Iraq.

On Monday, Bush criticized former secretary of state Hillary Clinton, the front-runner for the Democratic nomination in 2016.

"With their phone-it-in foreign policy, the Obama-Clinton-Kerry team is leaving a legacy of crises uncontained, violence unopposed, enemies unnamed, friends undefended, and alliances unraveling," he said.

Democrats made sure to remind voters of the George W. Bush's record.

"We already know what to expect from a Bush presidency, because we've seen it before. Jeb Bush supported his brother's disastrous economic and foreign policies that made us weaker at home and abroad," said Rep. Debbie Wasserman Schultz, head of the Democratic National Committee.