“It’s very uncommon to challenge incumbents — period. So this is truly unusual,” said Allan Lichtman, a professor of history at American University who has written about fissures in the conservative movement.

Primary campaigns against party leaders are often more of a nuisance than a serious threat, token challenges waged by local gadflies. But what is startling to Republicans this year is the sheer number of candidates who are willing to take on the party’s most powerful players in Washington, and the backing they are receiving from third-party groups.

The primaries are another measure of the internal tensions within the party, and the erosion of allegiance to it, as it seeks to maintain the enthusiasm of Tea Party supporters even as it tries to project a message with broader appeal to swing voters Republicans will need in the fall.

Mr. Lichtman said the best historical parallel was in 1938, when President Franklin D. Roosevelt tried to purge anti-New Deal conservatives from the Democratic Party.

The odds for an upset in any of the primaries this year are small. But the election will test whether the Tea Party, a force that has helped Republicans topple Democrats in local races across the country, has become more self-destructive than advantageous....