One of the early names raised as a potential candidate for the Senate seat vacated by Democrat Michael Rubio one week ago -- Assemblymember Henry T. Perea, D-Fresno -- has taken himself out of the running.

And that has prompted another potential candidate, Kern County Supervisor Leticia Perez, to rethink a run.

"While the opportunity to serve in the California State Senate is appealing, I made a commitment to my constituents to serve and meet the needs of my Assembly district," Perea wrote in a news release Friday. "I also made a commitment to my wife and family to create a balance between my home life and work. We are anxiously awaiting the arrival of our second child in July and I want to uphold my commitment to my family and the 31st Assembly District."

In her own statement, Perez said she had been supporting Perea for the seat.

"Given the news that Assemblymember Perea has now announced that he will not be running for this seat, we are experiencing an outpouring of support from constituents, supporters, volunteers, and Valley and statewide Democratic leaders to run for this seat," Perez wrote.

Kern County Democratic Party Chairwoman Candi Easter said she's behind Perez.

Perea's exit, Easter said, "opens the way for Leticia. We want somebody from Kern County."

But Perez, just two months into her first elected position as a county supervisor, remains uncertain about what she will do.

"This is not an easy decision, and my family and I recognize that we will face a mountain of criticism no matter what choice we make. This weekend I will be in close contact with my family, friends, and closest advisers to determine what is the right decision in these very unexpected circumstances," Perez said. "I will announce my decision after the Governor makes an announcement regarding the special election. Please keep my family in your thoughts and prayers."

Asked about another potential Kern County candidate -- Fran Florez, the mother of former state Sen. Dean Florez -- Easter said Fran Florez's election track record doesn't speak well for her.

Fran Florez lost general election bids for the 30th Assembly District seat to Republicans in 2008 and 2010.

"Do we want somebody who's already lost twice. I don't," Easter said. "I think we can get behind the best candidate."

Florez did not return a call seeking comment Friday. She was appointed to a paid position as a member of the California Medical Assistance Commission in 2011, according to The Sacramento Bee.

Her Twitter account Florez4Valley posted its first tweet Thursday. It stated that she was the only "candidate" with experience in Fresno and Kern counties.

Friday afternoon, after Perea's announcement, a tweet on the account called him "an exemplary member" of the Legislature and "a devoted father."

A Republican candidate has yet to emerge for the spot, although names have been bandied about.

Assembly Republican Leader Connie Conway told The Fresno Bee, through a spokeswoman, that she was not interested in running.

The Bee reported that former Republican Congressional candidate Andy Vidak of Kings County could be considering a run.

Republican Bakersfield City Councilman Russell Johnson said he has been honored to receive a ton of support for his potential candidacy, but he and his wife aren't yet making a decision on a run.