Despite facing long odds of capturing the seat in a special election, several Republicans are mulling runs to succeed Rep. Jane Harman (D-Calif.).

Redondo Beach City Attorney Mike Webb is "strongly considering" jumping into the race, according to the Sacramento Bee; former state Assembly candidate Nathan Mintz said he is "collecting information" about making a bid; and Republican Craig Huey is also considering a run, the Bee reports. 

Republicans operatives believe Mattie Fein, who challenged Harman in 2010, will run again.

Harman was named as the new head of the Woodrow Wilson International Center for Scholars on Tuesday. She's expected to leave her seat in March.

There's no shortage of candidates on the Democratic side either. Los Angeles City Councilwoman Janice Hahn officially entered the race on Monday. Other potential Democratic candidates include state Assemblywomen Betsy Butler and Bonnie Lowenthal, state Sen. Ted Lieu and Secretary of State Debra Bowen.

The upcoming special election will see the first use of the state's new top-two primary system in a congressional race. Under the new law, which was approved by California voters last June, the primary would be non-partisan with the top two vote getters advancing to a general election. But if a candidate gets over 50 percent of the vote in the primary, he or she wins the seat. The law is being challenged in court.

Some Republican strategists believe the party will have a better chance of capturing the seat in 2012, after redistricting is completed.