NEW ORLEANS — Tea Party thunder fills the Hilton Riverside ballroom with denunciations of President Obama and criticism of congressional Republicans for not being tough enough on him. The atmosphere has the energetic but hostile tone that helped propel conservatives to success in 2010.

Yet outside of this hermetic setting, where the Republican Leadership Conference was meeting this weekend, the political reality was sharply different: Incumbents are fending off Tea Party challengers in primary after primary, and the establishment is reasserting itself as the party’s center of gravity.

The ultimate test of its strength will come on Tuesday in Mississippi, where Senator Thad Cochran, a 76-year-old master of pork-barrel spending who is seeking a seventh term, will face a challenge from State Senator Chris McDaniel, who has attracted support from Sarah Palin, Rick Santorum and an array of conservative groups.

After the Mississippi results are in, Tea Party-aligned forces will have little opportunity to upend mainline Republicans, or even throw them much of a scare.