A March 3 special election in Southern California could give an early hint of Democrats’ chances of holding the House majority they won in 2018, and both sides know it.

Minnesota Rep. Tom Emmer, head of the National Republican Congressional Committee, said last month that Republicans had “a narrow path” to take back control of the House from the Democrats and that it involved grabbing four or five seats in California.

Not going to happen, answered Andy Orellana, a spokesman for the Democratic Congressional Campaign Committee.

In California, he said, “voters rejected Republicans in 2018 and will do so again in 2020.”

Last year, Democrats took the majority by grabbing 41 House seats from Republicans nationally, including seven in California.

But one of those new seats belonged to Katie Hill of Santa Clarita (Los Angeles County), who resigned from Congress on Oct. 31 after nude photos of her were circulated online and she was accused of having sexual relationships with a woman who worked on her campaign, which she admitted to, and a man on her congressional staff, which she denied.

The special election to fill the few months left in Hill’s term will be more than just a chance to choose a new member of Congress. Democrats and Republicans from across the country will be looking at the contest for an indication of how the political winds are blowing in advance of next November’s presidential election.

For Emmer, who takes a national view of the battle for the 218 seats needed to control the House, the answer is easy.

“The new socialist Democrat majority in the House literally gave away its majority the day it started this impeachment proceeding” against President Trump, he said in an interview for C-SPAN’s Newsmakers show. “The choice will be simple: freedom versus socialism.”

That’s not a theme likely to play well in California, where a November poll by the Public Policy Institute of California found more than half of California adults wanted to see Trump ousted from office.

Then there’s the election itself. The 25th Congressional District, which includes the Los Angeles County desert towns of Lancaster and Palmdale and extends west to Simi Valley in Ventura County, was a longtime GOP stronghold. But that has changed as younger voters from Los Angeles have moved north, looking for cheaper housing.

In 2018, Hill easily beat GOP Rep. Steve Knight, 54% to 46%, and the district’s Democratic registration edge has grown since that election.

That hasn’t stopped Knight from jumping into the primary for the November 2020 race for the full, two-year term. Also in the race are four other Republicans, including Mike Garcia, a former Navy aviator who has raised nearly $500,000 for the contest, and George Papadopoulos, a one-time foreign policy adviser to Trump’s 2016 campaign who pleaded guilty to lying to the FBI during the probe into Russian interference in the election season three years ago.

On the Democratic side is Santa Clarita Assemblywoman Christy Smith, who has been endorsed by Sen. Kamala Harris and other leading Democrats, and Cenk Uygur, co-founder of the progressive group Justice Democrats.

All the candidates running in the primary for the two-year term are expected also to run in the special election, which will be on same March 3 ballot. The first day for filing for the race is Dec. 23.

With that many candidates, it’s unlikely anyone will get the 50% plus one needed to win the special election outright. That means the top two finishers will face off on May 12, with the winner serving until the new Congress takes over in early January 2021.

If the Democrats make that May vote a repeat of 2018, with an easy win over the Republican candidate, it’s hard to see how things will change much by November, either in the district or, arguably, statewide. But if Republicans can win that special election, or even make it close, it will be an indication that targeted Democrats across the state could face a tough road to re-election.

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