TAMPA, Fla. — Mitt Romney arrives here this week to accept his nomination from the increasingly disparate coalition of factions known as the Republican Party, confronting the challenge of unifying them behind him and — should he win — exerting his own authority over a party that is in many ways still forging a post-Bush identity.

In interviews, Republican leaders said they were united and energized by the prospect of defeating President Obama and enacting bedrock Republican principles: shrinking the government and reducing spending and taxes.

At the same time, many said they were concerned about the crosscurrents that have churned the party, particularly since the emergence of the Tea Party movement three years ago. And on Sunday, thousands who supported the presidential campaign of Representative Ron Paul of Texas rallied here to challenge what they view as business as usual among Republicans.

Some leaders expressed worry that the turn to contentious social issues in the days leading up to the Republican National Convention, where the party platform is likely to embrace a tough anti-abortion stance and strict curbs on immigration, could undercut the party’s need to broaden its appeal. Many of them said they feared it was hastening a march to becoming a smaller, older, whiter and more male party.