Anger among women over Judge Brett Kavanaugh’s nomination to the U.S. Supreme Court is threatening to turn what’s already a gender gap in a number of California congressional races into an anti-GOP chasm, a new Democratic-backed poll has found.

In four Republican-held districts in and around Orange County, women say they are dramatically less likely to back GOP candidates if Kavanaugh is confirmed, according to a poll done by Change Research for the Democratic group Fight Back California and the California Labor Federation.

“These are extraordinary numbers,” said Katie Merrill, chief strategist for Fight Back California. “Kavanaugh is a very powerful factor in swing districts, especially among suburban women.”

Merrill’s political action committee, founded by former East Bay Democratic Rep. Ellen Tauscher, is working to flip GOP-held California congressional seats. The seven or more targeted districts in the state make up a major chunk of the 23 seats nationwide that Democrats need to take control of Congress.

The poll numbers for likely female voters alone already are daunting for Republicans in those Orange County-area districts. Even in the three districts where Republican women are running, the Democrats opposing them are leading among female voters, the poll indicates.

Democrat Gil Cisneros has a 58 percent to 39 percent lead among women over Republican Young Kim in a district now held by retiring GOP Rep. Ed Royce of Fullerton. Democrat Katie Porter is beating GOP Rep. Mimi Walters of Irvine, 53 percent to 42 percent.

In the district now held by retiring GOP Rep. Darrell Issa of Vista (San Diego County), Democrat Mike Levin holds a 59 percent to 36 percent lead among women over Republican Diane Harkey.

In the fourth district in the poll, Republican Rep. Dana Rohrabacher of Costa Mesa is losing to Harley Rouda among women, 56 percent to 43 percent.

That Democratic support could grow if Kavanaugh is confirmed. A Senate vote could come as soon as Saturday.

For example, 43 percent of female voters in Walters’ district said they would be more likely to vote for Democrats if Kavanaugh is put on the court, while only 23 percent say that would give a boost to the Republican.

The gender gap already is worrisome for California Republicans. A study by the Public Policy Institute of California found that 52 percent of California’s likely voters are women. Exit polls in the 2016 presidential election found that 66 percent of California’s female voters backed Hillary Clinton over Republican Donald Trump. Overall, Clinton won 61 percent of the state vote.

“Women already are more likely to vote,” said Merrill, a veteran Democratic consultant. “Since those districts already have a Republican registration advantage, you have to believe that a significant number of Republican women are planning to vote for Democrats.”

The surge of female votes for the Democrats makes a major difference in the projected outcome. When the results include both men and women among likely voters, Republicans Rohrabacher and Kim are tied with their Democratic opponents, while Democrats Porter and Levin hold narrow leads.

A majority of women in each of the four congressional districts believe Kavanaugh lied to the Senate Judiciary Committee and are angry at the way Christine Blasey Ford, who has accused Kavanaugh of sexually assaulting her when they were both teenagers, has been treated during the confirmation process.

“Women in these districts are motivated to vote by Kavanaugh, and that should scare Republicans,” Merrill said.

The National Republican Congressional Committee, which is backing the GOP candidates in all four of those contests, could not be reached for comment.

The online poll was conducted Oct. 2-3 and was corrected to attain a sample reflective of the electorate in each district, according to Stephen Clermont of Change Research. The poll included 1,265 likely voters, including 655 women. The margin of error for the women interviewed is plus or minus 3.8 percentage points.

A new poll by the UC Berkeley Institute of Governmental Studies also showed Democrats generally on top, although not by much, in many of those contested GOP congressional races.

The survey, done by pollster Mark DiCamillo, found Democrats leading in races against Rep. Jeff Denham of Turlock (Stanislaus County), and Rep. Steve Knight of Lancaster (Los Angeles County), as well as in the contests against Kim, Walters and Harkey.

Rohrabacher was tied with Rouda, while GOP Rep. Devin Nunes of Tulare had a 53 percent to 45 percent lead over Democrat Andrew Janz.

In San Diego County, Republican Rep. Duncan Hunter, who is facing federal charges of misspending campaign funds, held a narrow edge against Democrat Ammar Campa-Najjar.

John Wildermuth is a San Francisco Chronicle staff writer. Email: jwildermuth@sfchronicle.com Twitter: @jfwildermuth