Representative Duncan D. Hunter, a Republican in San Diego who is also a Democratic target, issued a statement after Mr. Issa’s announcement, declaring that he is “100 percent running.” But Mr. Hunter is under investigation by the F.B.I. on allegations of misusing campaign funds, making him particularly vulnerable, officials in both parties said, and there is speculation in political circles that he ultimately will step aside. (If Mr. Hunter did step aside, that would probably increase Republican chances of holding the seat, given his party’s registration advantage there.)
The turmoil comes as California has emerged as the front line in Democratic efforts to win back the House. Seven of the 14-member Republican congressional delegation represent districts that Hillary Clinton won against Mr. Trump in 2016, including Mr. Issa and Mr. Royce. The party needs to capture 24 Republican seats to win back power. Democrats began recruiting candidates, raising money and setting up field operations here nearly six months ago.
Mr. Trump’s disapproval rating among independent voters, whose support is critical for any Republican hoping to win, shot up 20 percentage points from the week after his inauguration to the end of last year, from 48 percent to 68 percent, according to the Public Policy Institute of California. Independents make up 25 percent of the California electorate, a decimal point less than Republicans.
The president had a 73 percent approval rating among California Republicans in a poll last month by the Institute of Governmental Studies at the University of California, Berkeley, which, while high, was still considerably below what Barack Obama enjoyed among Democratic voters when he was president.
Mr. Trump and congressional Republicans have championed a tax bill widely assailed as punishing to California homeowners, dismantled policies aimed at fighting climate change and pushed tough and restrictive immigration policies. Last year, Californians voted to legalize recreational marijuana by a hefty margin of 57 percent to 42 percent; days after the law took effect on Jan. 1, the Justice Department announced it would aggressively enforce federal strictures against the drug.
The Interior Department moved last week to allow offshore oil drilling, a policy that has a long history of bipartisan opposition among Californians. The next day, it exempted Florida from the policy in response to pleas from Rick Scott, the Republican governor running for Senate, drawing accusations that the Trump administration was punishing this state.
“Most days for California Republicans in Congress are days spent on defense,” said Bill Whalen, a research fellow at the Hoover Institution and a former senior adviser to Pete Wilson, a Republican governor. “Defense spent on why Donald Trump wants to pull the country out of the Paris accords. Defense trying to explain why the president won’t give the same offshore drilling waiver to California as it did to Florida. And defense trying to explain the latest thing Donald Trump said that he’s now denying that he said.”
Mr. Chávez said he would not have voted for the tax bill and opposed the tough immigration policies backed by some Republicans in Congress. “Offshore drilling — I don’t support it,” he said. “I’ve been in California my whole life. I remember the Santa Barbara spill.”
For all that, Republicans have some reason to hope they can withstand any Democratic wave. The fact that Mrs. Clinton won districts represented by these seven Republicans does not mean that voters will necessarily support a Democratic candidate for Congress in November. Although Republican enrollment in this state has been on a steady decline, the party continues to have a registration edge in these districts. Historically, Democratic turnout drops in nonpresidential years — especially in California.
“As a 34-year resident of Irvine in Orange County and as someone who has long been active at a variety of levels in political and policy debates, I am also reluctant to conclude that Democrats in a midterm election will be able to turnout a sufficient number of voters to overcome the current advantages Republicans still have in the districts,” said Mark P. Petracca, a professor of political science at the University of California, Irvine.
Jim Brulte, the California Republican leader, said voters made their decision based on the candidates, not the party. He said he did not think Mr. Trump was an albatross on his candidates.
“Look, Republicans lost every statewide race in California in 2002, 2010 and 2014, before Donald Trump even announced he was running for president,” Mr. Brulte said. “So anybody who wants to blame Donald Trump for the problems of the Republican Party, which began 20 years ago, is a revisionist historian.”
It has long been a tough climb to get elected as a Republican in California. But Mr. Trump’s presidency has pushed a party already struggling closer to the brink. Republicans and Democrats said that the level of anger at Mr. Trump could very well push up Democratic turnout in these districts.
“It was already difficult,” said Rob Stutzman, a Republican political consultant in Sacramento. “But he’s made it more difficult.”
Mark Baldassare, the president of the Public Policy Institute of California, said Mr. Trump’s stand on issues “has been at odds even with many Republicans” in the state, “especially on immigration.”
“In our polling, we have seen majorities of Republicans saying they want a path to citizenship,” he said. “They support DACA,” the Deferred Action for Childhood Arrivals program, which protects so-called Dreamers from deportation.
The offshore drilling policy was the latest complication for Republican candidates. In a poll taken in 2017 by the Public Policy Institute, 69 percent of respondents said they opposed opening up offshore sites for drilling. Republicans were more supportive — 50 percent said they backed it — but majorities of Republicans who live near the coast opposed it. Mr. Issa’s district runs along the coast.
Last week, moderate Republicans, including Arnold Schwarzenegger, the former governor, announced they were creating an organization intended to try to save the state party, in part by differentiating it on issues like immigration and climate change.
“What works nationally doesn’t work in California,” said Chad Mayes, a State Assembly member and one of the founders of the group. “We are in a death spiral. We have to get out of this death spiral.”
Mr. Trump is a historically weak political figure here. He drew 31.5 percent of the vote against Hillary Clinton, an even poorer showing than Herbert Hoover posted when he ran against Franklin D. Roosevelt in the midst of the Depression.
And he poses a challenge to Republican candidates for state and federal office who need the votes of the Republican base, who support Mr. Trump. The result: Candidates have spoken warmly about Mr. Trump at forums where they need to win Republican support.
“Californians are waking up to one of the best economies we have seen in decades, since Ronald Reagan was president,” said Travis Allen, a Republican State Assembly member who is running for governor. “The Trump effect on the economy is being felt across the country — even in California. I fully expect this to continue and to be a huge benefit for every Californian.”
Mr. Whalen of the Hoover Institution said that Mr. Trump “is not the person with whom you are going to identify the future of the party.”
“But what do you do?” he said. “You can’t walk away from him.”
Mr. Stutzman, the political consultant, said it would be difficult for the state party to recover as long as Mr. Trump is in the White House: “The degradation of the Republican brand in California cannot be reversed with Trump as president.”