Gov. Arnold Schwarzenegger told the Los Angeles Times today that he is “not running for anything,” meaning he won’t run for Barbara Boxer’s U.S. Senate seat, next year.

The statement came just a few weeks after he fueled speculation — and incited a few chuckles — in an offhand remark that seemed to leave the door open for a run against Boxer:

“I have my hands full with all the stuff I’m doing now,” he said, referring to his campaign to pass a package of budget-related propositions that are on a special-election May 19 ballot. “I’m concentrating on that and not what I’m going to do next,” he said.

“You know,” he added, as he signed autographs, “I’m not a politician. I’m a public servant.”

With his polling down in the low 30s for months now, as they were in 2005, some in the state have speculated that what the governor meant to say was, “I am not a good politician.”

The only people pushing Schwarzenegger to run are national Republicans in Washington who like his 100 percent name recognition and access to cash. What they don’t seem to grasp is that Schwarzenegger has a nearly insurmountable problem in the state: He has no base among California voters.

The state’s hard core GOP distrusted and disliked Schwarzenegger because of his liberal ways before he broke faith with them and proposed raising taxes as part of his plan to eliminate the state’s $42 billion deficit. In the Times interview today, the governor cited his broken pledge as a central reason he will not run.

Conversely, moving to the left has not helped Schwarzenegger among Democrats, who outnumber Republicans by a strong margin, and whose trust he has never had or even tried hard to win. He seems to be popular with a certain stripe of independent voters, but they are not eligible to vote in primaries, a fact that would put Schwarzenegger’s fate in the hands of the hard-core Republicans, whose votes could easily be siphoned off by an extreme right-wing tax hater like Rep. Dan Lungren or Rep. Tom McClintock — either of whom Boxer would likely beat handily.

(This is precisely what happened in the 1999 governor’s race, when liberal Republican Richard Riordan, the former mayor of Los Angeles, was knocked out in the primaries by right-wing featherweight Bill Simon, who was then trounced by Democrat Gray Davis in the general.)

Until earlier this month, the most likely candidate to run against Boxer was Carly Fiorina, the former CEO of Hewlett Packard who is remembered in the Silicon Valley for her disastrous handling of the merger of HP with Compaq — and for the $20 million reward-for-failure she was given on her way out the door. More recently, she created a stir in last year’s presidential campaign with a series of foot-in-mouth gaffes for which she was unceremoniously excised from the McCain campaign. On March 3, however, it was announced that Fiorina, who is 54, had been diagnosed with breast cancer, a factor that will likely put her political aspirations on hold until after her recovery.

Sen. Boxer’s polling has been anemic since last year, in part because Californians were unhappy with their delegation’s complicity in letting George Bush off the hook. However, with no big-name competitor, she may find herself in a race very much like her last run, in 2004, when she received the third highest number of votes of any candidate in the nation, under George Bush and John Kerry.