WASHINGTON — In the wake of their electoral drubbing in November, Republicans sought an image reboot at President Obama’s State of the Union address, a new face that would be both more positive and less strident, youthful and multicultural but also quietly constructive and respectful.

Then there was Ted Nugent, the 64-year-old rocker who once told the president to “suck on my machine gun.”

Mr. Nugent, the gun-rights brawler, sat stone-faced high up in the House spectators’ gallery as the president pressed an agenda that went far beyond gun control. Invited to watch as the guest of another firebrand, Steve Stockman, a Republican representative from Texas, his crossed arms and stern visage seemed to capture the conflict still lurking within the Republican Party as its leaders look to expand their appeal.

There were no shouts of “you lie!” Tuesday night, no overt moments of disrespect beyond the usual partisan responses to policy. But in a House chamber filled conspicuously with the victims of gun violence and family members still grieving for lost loved ones, Mr. Nugent seemed like a provocation, a saber-toothed tiger invited to a garden party.