A field of Republican candidates for the United States Senate and governor is struggling against these headwinds as they seek to end a more than 10-year drought and elect a party member to statewide office. Under the California election system, candidates compete in an open, nonpartisan primary on June 5. The two candidates who get the most votes — regardless of party — advance to the November general election.

If Republicans fall short in capturing one of those two November slots next month, which members of both parties say is a strong possibility, it would apparently be the first election where there was no major party candidate for both the Senate and governor races since 1914.

“Maybe hitting rock bottom is getting shut out of both state races this year,” said Bill Whalen, a research fellow at the Hoover Institution and a former senior adviser to Pete Wilson, a Republican governor. “You would think that if Republicans are shut out, it will be time for some serious soul-searching.”