CHARLOTTE, N.C. — The next round of Republican primary fights is not far away, which prompted Gov. Bobby Jindal of Louisiana to offer a blunt warning this week: “We’ve got to stop being the stupid party.”

With bruising defeats from the last two election cycles still fresh in his mind, particularly the races that helped cost Republicans control of the Senate, Mr. Jindal’s stern message to his party highlighted the divisions among Republicans as they try to restore their brand and rebuild.

The critiques many Republicans have about their party are rooted in the divisive primary campaigns that have knocked out veteran lawmakers, only to produce flawed candidates who have uttered highly charged statements that have alienated many voters.

The challenge was highlighted anew on Friday as Senator Saxby Chambliss, Republican of Georgia, announced his intention to step down next year. In doing so, he avoids a contentious ideological battle that has toppled several fellow Republicans seen in Washington as steady and valuable members of the party’s mainstream.

The difficulties facing the Republican Party are framed by Mr. Jindal’s urgent plea, which he delivered here Thursday evening to a meeting of the Republican National Committee, and the retirement of Mr. Chambliss. Mr. Chambliss had faced bracing criticism — and a possible primary challenge on his right flank — for his work with Democrats to find a bipartisan deficit reduction plan that would have included added tax revenues as well as spending cuts.

Party elders also argue that the recurring fiscal brinkmanship in Washington has been wrongheaded for Republicans, who often seem to be willing to risk the nation’s economy simply to get their way. At the same time, some Republicans expressed dismay at the inability of conservative House members to see the end-of-year tax deal as a victory since it made permanent nearly all the Bush-era tax cuts, though it raises taxes on the most affluent.

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