WASHINGTON — Democrats enhanced their prospects for winning control of the House in Tuesday’s coast-to-coast primaries, skirting potential calamity in California and lining up likely gains in New Jersey.

But Republicans avoided their own worst-case scenario, securing a spot in the California governor’s race, which should help bring Republican voters to the polls this fall. They also chose strong candidates in Southern California for the showdown in November.

It was the Democratic Party, however, that feared disaster in California, where a quirky “jungle primary’’ gives the November ballot to the top two finishers in the primary, regardless of party. Democratic contenders leveraged financial and strategic help from the national party to weather the winnowing primary, and ensure that they will field candidates in multiple California House districts that they will most likely need to win control in November.

“Even though Democrats had to spend a few million dollars, crisis averted,’’ said Nathan Gonzales, a veteran House race handicapper and the editor of the Inside Elections newsletter.

The party will now be able to mount challenges in places where it feared being shut out, including open seats near San Diego and Los Angeles and districts represented by Republican incumbents in Orange County and Los Angeles County, and around Modesto. Between California and New Jersey, Democrats will contend for at least 10 Republican-held seats, nearly half of the 23 they need for control.

Republicans saw some positive developments Tuesday as well. In the California governor’s race, John Cox, a Republican, secured a spot on the ballot to face Gavin Newsom, the Democratic lieutenant governor. Republicans are unlikely to have a general election candidate against Senator Dianne Feinstein on the ballot, and a failure to field challengers for both offices at the top of the ticket could have been devastating for Republican enthusiasm and turnout in the state.

In an early-morning tweet Wednesday, Trump embraced Cox and tried to counter the widely prevailing view that Democrats had dodged an electoral bullet.

“Great night for Republicans! Congratulations to John Cox on a really big number in California. He can win,’’ Trump tweeted. “So much for the big Blue Wave, it may be a big Red Wave. Working hard!’’

In addition, congressional Republicans were enthusiastic about their own contenders in California, including Young Kim, a Korean-American woman who was the top vote-getter in the primary to replace US Representative Ed Royce, another retiring Republican in a district that is nearly 30 percent Asian.

“As a businesswoman and a longtime aide to Congressman Ed Royce, Young understands Southern California families’ needs,’’ said Representative Steve Stivers of Ohio, chairman of the National Republican Congressional Committee.

Another female candidate, Diane Harkey, was the top vote-getter in the San Diego County district being vacated by Representative Darrell Issa.

While Democrats managed to push their candidates through the dicey process, their success in the California races is not guaranteed even though at least seven Republican-held districts in play were carried by Hillary Clinton in 2016. Despite some opposition to Trump, the districts remain dominated by Republican voters. And Democrats did not always get their preferred candidate, with the more liberal candidates prevailing in some districts.

For instance, Democratic voters in Orange County picked Katie Porter, a law professor and strong progressive candidate, over more business-oriented Dave Min to face Representative Mimi Walters, a Republican in her second term, in November. Orange County, south of Los Angeles, has never been known as a bastion of liberalism.

“I’m not convinced that voters are going to punish Mimi Walters and Dana Rohrabacher because they don’t like the president,’’ said Gonzales, referring to two California Republican incumbents at risk.

Democrats were threatened by an embarrassment of riches in California arising from a strong backlash against Trump. The environment created a golden opportunity to win a seat in Congress, and the prospect attracted so many contenders in some cases that the party feared the candidates would divide the vote and open the door to Republicans winning the top two slots.