Yet in the “be careful what you wish for” department, Democrats are beginning to confront the struggles and complications that come with being in charge of the store. This authority came at least two years earlier than most Democrats had projected. And it is unleashing years of pent-up Democratic desires — to roll back spending cuts, approve a bond issue to rebuild the state’s water system, amend the state’s tax code, revamp California’s governance system — that had been largely checked by the Republican minority.

At the same time, it is stirring concerns from Democrats, among them Gov. Jerry Brown, that the situation may inspire an overreach that could make the party’s reign brief. By contrast, some Democrats argue that handled correctly, the next two years could provide an opportunity to lock in long-term control.

“The center of gravity of the Democratic Party will be restraint, but some people can’t help themselves,” Mr. Brown said in an interview. “The supermajority is not a permanent condition. It’s something that can be lost far more easily than it can be gained.”