In a radio interview, Republican Party spokesman Rob Stutzman on Wednesday said the star of the "Terminator" movie series had decided not to run in the 7 October vote.
Privately, Republican officials fumed that the actor was dragging out his exit from the political stage. "This is sucking the life out of the fact that Democrats are falling apart," one said.
Schwarzenegger aides have said that the actor was leaning hard against making a run because of his desire to spend more time with his four children who are aged five to 14. Some analysts say the sensitive actor may also be wary of subjecting himself to a tough campaign's personal attacks and rumours.
"This is sucking the life out of the fact that Democrats are falling apart."
--Unnamed Republican official
Democrats have tried to temper whatever relief they may feel about not having to face Hollywood's 'Terminator'.
"I haven't seen anything in the polls that would suggest he is a major threat, although of course he has a big name and on a low turnout day, you cannot underestimate that power," Rep. Nancy Pelosi, House Democratic leader, said.
The action hero and former bodybuilding champion had hinted heavily in recent weeks that he would run in an unprecedented ballot on whether voters want to unseat Democratic Governor Gray Davis.
But his aides said his wife Maria Shriver, a niece of former President John F. Kennedy, opposed his entry into politics.