The first step for the candidates running in next year's California Senate race is to quietly try to spook newly appointed Sen. Laphonza Butler into not running at all.

Advisers to the campaigns of Reps. Barbara Lee, Katie Porter and Adam Schiff all say that they are giving Butler time and space to decide. They each issued statements praising her -- albeit gradually. Schiff was in the Senate gallery for Butler's official swearing-in on Tuesday, and Lee attended a ceremonial Congressional Black Caucus swearing-in shortly after on the other side of the US Capitol. (Porter texted with Butler earlier in the day to express regrets about a meeting she couldn't move, and Butler texted back to say she understood, according to an aide.)

But while they briefly paused public politicking until after the Sen. Dianne Feinstein's funeral on Thursday -- with Lee and Schiff flying there on Air Force 2 -- they spent even this past week preparing to ramp up new endorsements and outreach that they hope will convince Butler there is not enough time to mount a credible campaign, and that she could risk being known now for her historic appointment to serve the remainder of the late senator's term through January 2025 to being known for coming in third, fourth or even fifth in a race that has its first round on March 5. (The top two candidates, regardless of party, move on to a November election, and the race is set to get another wrinkle next week, when former Dodgers and Padres first baseman Steve Garvey is expected to launch his campaign as a Republican.)

Butler had a meeting with a small group of advisers the day after being sworn in to do a preliminary review of polling data as part of what people familiar say is a push to make a decision by next week.

Every day that goes by, many people in California political circles agree, is a day that Butler is even further behind politically if she's going to go for it.

Butler's new temporary spokesperson keeps providing the same statement about how she has not made a decision yet. But Butler is well-known among California insiders, with top Democrats in the state telling CNN, "She does not do things that she cannot be successful at -- so my guess is she would not have put herself in this spot if she didn't think she had a shot at winning an election."

According to CNN's conversations with nearly two dozen officials and operatives deeply involved in the appointment and the Senate campaigns, they are all left guessing. That includes Gov. Gavin Newsom himself, according to a spokesperson; he doesn't know what her decision will be, though he has said publicly that he offered the appointment to Butler with no strings attached.

"It's uncomfortable and weird waiting this out," said an operative working on one of the campaigns who asked not to be named. "I just don't see how anyone in the next five months is able to mount a campaign that can work."

None of the campaigns are just sitting around.

Lee -- who went from hoping for the appointment to, in recent weeks, making a political issue out of knocking Newsom on the assumption she wouldn't get it -- spent Monday and Tuesday reaching out to fellow members of the Congressional Black Caucus to urge them to stick with her, even though there is now another Black woman in the spot. Schiff's initial response was to trumpet the big lead he has in fundraising, which aides were hoping would get both Butler's attention and that of reporters busy assessing her chances. California political insiders have noticed anti-Butler opposition research appearing and a new anti-Butler account on X, and have been pointing fingers over who is behind them. False rumors that Newsom offered others the appointment first have been floated, too.

"If she runs, that won't change what we do anyway," said one person working with Lee. "The more candidates in the race, the more your calculations change in terms of what you need to win. Having the appointed senator in the race with the title 'appointed senator' will clearly have some impact -- nobody will know how much until you get into it."

A spokesperson for Butler declined comment when asked about her deliberations, including the meeting to discuss polling.

Multiple clocks ticking on Butler at once

All the activity has angered some of the people excited by Butler's appointment, including former San Francisco Mayor Willie Brown, who told CNN in a phone interview that he thinks that people should be applauding Butler not just as a fulfillment of Newsom's promise to appoint a Black woman, but for her accomplishments.

"Everybody said they wanted a Black senator. They did not say 'Black Willie,' 'Black Barbara,' 'Black Andy,'" Brown said. "This woman is as Black as you get. You either adhere to that or you were bullshitting when you said it."

Brown, who is Black himself, said he would like to see the other candidates drop out now that Butler is the third Black female senator in United States history. "Everybody ought to embrace that," he said. "Why wouldn't we be demanding that she runs?

Brown's advice to Butler was to quickly go on the offensive: "First thing she should do is call Adam Schiff, call Barbara Lee and call Katie Porter -- call them all and ask for their endorsement."

Butler has multiple clocks ticking on her at once: She has to build a new staff out of the people who had stayed on as caretakers for the long-ailing Feinstein; she has to start making public appearances in the hopes of getting attention in a big state where her name ID is effectively zero; and she has to do it all while learning a complicated job in the middle of what could grow into a full-blown congressional crisis in the aftermath of former House Speaker Kevin McCarthy's defenestration, all without any prior experience in office.

If Butler does run, she faces a soft deadline of October 13 to submit her name to the state Democratic Party to be considered a candidate for its endorsement, as well as a mid-November state Democratic convention. Those come before the December 8 deadline to officially declare herself a candidate for the ballot. And then, on top of everything else, she would have to start building up political outreach and planning fundraising events to put together many millions of dollars she is already behind on.

"She's a strong candidate. She's smart," former California Gov. Jerry Brown, a Democrat who years ago appointed Butler to the state board of regents, told CNN in a brief phone interview. "I think she'll be a real addition to the US Senate."

But Brown said it's too early still to get a sense of how Butler would do in a race to hold on to the seat.

For someone who has never held office before, Butler has enormous connections with many of the most important Democratic constituencies -- and not just because she is the third female Black senator and only the second openly gay sitting senator. Newsom considered hiring her as chief of staff years before he made the Senate offer. She served as a major labor leader in the state and worked with many of its top officials, including Kamala Harris, in her roles both as senator and as vice president.

Butler also is tapped into a massive fundraising network from her past two years as president of the Democratic women's political empowerment and pro-choice group EMILY's List. She is set to be the new featured speaker at a major Friday luncheon for the group in New York as her first big public appearance since being sworn in.

Several California political insiders speculated that a fundraising disadvantage could be overcome if a few wealthy donors funded an independent expenditure effort on Butler's behalf, especially given that even Schiff's $32 million head start isn't that much in a state where campaign operations and television commercials are so expensive.

But breaking through in California is extremely difficult. The three members of Congress each have concentrated followings, and both Schiff and Porter have email lists swelled with active Democrats from years of very public battles with Donald Trump and Republicans in Congress. For months after his own appointment by Newsom to the state's other Senate seat in 2021, Sen. Alex Padilla's name recognition in the state was stuck in the teens -- and that was after two decades of working his way up in other elected offices.

A private poll of the California Senate race conducted on Sunday and Monday has been working its way through the inboxes of state Democratic operatives trying to gauge Butler's support. It shows many people undecided about whom to support and open to Butler when they learn more about her.

The pollster, Christian Grose, told CNN he isn't working for Butler or any of the other candidates, and that when he conducted it, he was assuming Butler wouldn't run. But when he asked people to pick a candidate from a list of names, the number of people who said they would go with her was so low it amounted to statistical "noise."

Pushback from the Congressional Black Caucus

A day after caveating her post on X congratulating Butler by writing that she was looking forward to "having two incredible Black women serve consecutively when we elect Barbara Lee as the next Senator from California," Massachusetts Rep. Ayanna Pressley posed for pictures with Butler, Lee and several others in front of the Rosa Parks statue in the Capitol to welcome the new senator to the Congressional Black Caucus. Shortly after, Pressley stood outside the Capitol and told CNN, "I'm celebrating both women."

"I'm not going to allow anyone to rob me of that joy and to pit any of us against one another," she added.

Many of Lee's CBC colleagues are already sticking by her.

"As far as I know, there's only one Black woman that is running in the primary, and that's Barbara Lee," New York Rep. Greg Meeks, the chair of the CBC's PAC, told CNN on Tuesday.

Whether Butler should run, Meeks added is "up to her, and the people of California, but the Congressional Black Caucus' and the Congressional Black Caucus' PAC's candidate is Barbara Lee."

Rep. Emanuel Cleaver, a senior CBC Democrat from Missouri, was more blunt, saying he could not understand Newsom's "unfortunate" decision. In talking about Butler, he could not remember her name.

"I hope that she won't run, for a lot of reasons," Cleaver said, listing Butler's lack of legislative experience as one of them.

Of course, none of them are California voters. Rep. Sydney Kamlager-Dove, a freshman congresswoman from Los Angeles who was also at the ceremonial CBC swearing in, said of Butler, "She's a consensus-builder, she is inspirational, she is strategic, she certainly understands this work."

Kamlager-Dove made a joint endorsement of Lee and Schiff earlier in the year but said she is now waiting to make her next move until the end of the year, when she can see "who really is running."

As for Butler, "I want her to get her sea legs, I want her to acclimate to this new environment and then make a decision if this is something she wants to do for the long term. People don't understand how upending this work can be when you have a family, when you have a family and you're located in California," Kamlager-Dove said, adding, "If she wants to run, I want her to run."

If Butler does decide to vie for the seat, Kamlager-Dove said she is open to switching her endorsement -- but that would start with the grinding work that consumes the days of anyone campaigning.

"She'd have to call," Kamlager-Dove said, "and ask me."