She simmered as efforts to tame California's $26.3 billion deficit threatened to shred the health and welfare safety net she helped stitch together as a Democratic lawmaker from Los Angeles. She stewed in budget briefings as clear second banana to Darrell Steinberg, D-Calif., her counterpart in the state Senate. Finally, she boiled over at Gov. Arnold Schwarzenegger. He rankled Democrats with demands that could undermine their union allies and a declaration to The New York Times that he was 'perfectly fine' despite the fiscal meltdown, ready to enjoy an evening cigar in his Jacuzzi. The Assembly's den mother became a growling bear, griping after an unsuccessful budget session between legislative leaders and the governor that Schwarzenegger 'broke it. He should fix it.' That rare outburst earned an ovation from her Democratic caucus. But Bass has no time to be sanguine. A few Capitol insiders say that barely a year into her tenure, attempts to topple Bass are inevitable. Her critics say she has a wishy-washy administrative style and is politically tone deaf. They fault her for one of the year's biggest political blunders -- hiking salaries for legislative staff a few weeks before the May 19 special election. The finance measures on that ballot failed, putting the state deeper in the hole. 'I will be shocked if she's still around by Sept. 1,' said one longtime legislative staffer. Bass brushes off such assessments as 'the nature of the beast.' Coup rumors have bedeviled her since May 2008, when she became the first black woman in U.S. history to lead a state legislative house. 'When it comes time to leave, it will be in a natural order' and not before early next year, Bass said Tuesday in her ornate office hugging the Capitol's northwest corner. Even some of her rivals concurred. 'I actually like her more in the last week or so,' said Assemblyman Charles Calderon, a Democrat from Montebello, who has often jousted with Bass over policy and politics. 'She clearly has made some mistakes, some very large mistakes. But she is speaking up and standing up for us. I believe she is going into her best moment.' Still, by her own admission, Bass, 55, has enjoyed few such moments during her crisis-plagued stint as Assembly leader. She inherited a fractured caucus that her predecessor, Fabian Nunez, corralled with a mix of power politics and charm. Bass was the anti-Nunez, a genial facilitator reluctant to mete out punishment and bully fellow members, many of them Type-A overachievers. Some have been bothered by her refusal to play hardball with the governor, especially after he began proposing cuts in health and human services. Finally, when the governor stepped in last week and worked with GOP lawmakers in the Senate to block a Democratic deal to delay the onset of IOUs, Bass peeled back her normal calm. She conspicuously missed a Monday morning meeting of legislative leaders with the governor, then held a news conference to talk about it. She accused Schwarzenegger of shifting the rules mid-game with new demands. Sitting in her office a day later, Bass dismissed her absence from the meeting as 'much ado about nothing,' said she would not miss another such session and held out hope that she and the governor could eventually see eye to eye. 'The last thing in the world I want to do is have a war with the governor,' Bass said. 'I'm a goal-focused, product-oriented person. And I want this situation to stop.' Schwarzenegger has refused to take on Bass directly, calling her 'a great public servant' who is 'passionate about what she's doing.' Bass has a convivial relationship with Steinberg, who has at least two advantages -- more legislative experience and more time to rule. Bass will be forced out of the Assembly next year; Steinberg won't face his term limits until 2014. His resume includes a stint in the Assembly that has given him a half-dozen more years in the building. And Steinberg, who is also struggling with a restless caucus, has taken a different approach to the budget fight. He resigned himself early to unbending GOP resistance to tax hikes. And his continued efforts to engage the administration even as the governor threw more demands on the table have muted Bass' battle cries. The governor has demanded that any budget agreement include policy changes that organized labor groups find unacceptable. Some of them would shrink the state's in-home health-care program. The unionized workers in that program pay millions of dollars monthly in dues to the Service Employees International Union, one of the biggest donors to legislative Democrats. Those include Bass, by tradition the key fundraiser for her caucus. Bass also risks falling out of favor with the California Teachers Association, a potential career killer for any Democrat. Some experts say it may be impossible to balance the budget without suspending voter-approved school funding guarantees that the union holds sacred. 'If they have to give in, CTA will be furious, and fingers are going to point very quickly,' said Larry Gerston, a San Jose State University political scientist. 'To the extent the Democrats need someone to blame when they sit in the ruins, the logical thing is to blame the speaker.' Times staff writer Evan Halper contributed to this report. 