California Gov. Arnold Schwarzenegger speaks at a news conference Wednesday, Aug. 27, 2008, in Los Angeles. Schwarzenegger said Wednesday he will remain in California during the GOP convention if lawmakers fail to reach agreement on a state budget, now two months overdue.

SACRAMENTO, Calif. — When the Republican convention opens Monday night, its prime-time lineup could be missing one of its biggest draws: California Gov. Arnold Schwarzenegger.

Shackled by the mundane business of state government, Schwarzenegger is vowing to remain in California if lawmakers fail to reach agreement on a state budget, now two months overdue.

“The work for the people of California, and to solve this budget problem, is the most important thing right now for me,” Schwarzenegger said Wednesday during a news conference in Los Angeles.

A budget deal by showtime seems unlikely at this point, potentially costing Schwarzenegger a national platform and McCain a high-profile supporter who has been popular with the kind of independent voter McCain hopes to attract.

Schwarzenegger’s absence also would be a letdown for the TV networks, which would lose one of the biggest potential draws on the convention’s opening night. Other speakers scheduled for Monday include President Bush, Vice President Dick Cheney and numerous members of Congress.

Schwarzenegger’s failure to commit is proving to be a source of frustration for convention organizers, who like to nail down their programs well in advance. Given the star power of the actor turned politician, they’ll still squeeze him into a prime slot if they can get him.

The stalled budget already forced Schwarzenegger to curtail nearly all appearances this summer. His efforts to cajole lawmakers into a compromise have repeatedly fallen flat.

California is the only state with a fiscal year beginning July 1 that has not approved a spending plan.

Lawmakers remain at odds over how to close a $15.2 billion budget gap, with Republicans adamantly opposed to any tax increases and Democrats seeking to avoid massive program cuts.

Most Democratic lawmakers already made the decision to stay home and miss their historic convention in Denver this week. The majority party likely won’t be motivated to strike a deal with their Republican counterparts in time for them to attend next week’s GOP convention.

Organizers of the St. Paul, Minn., convention still hold out hope that Schwarzenegger will show. Because his speech is scheduled for the Labor Day holiday, he could fly in and out on his private jet without missing any state business.

“We recognize his responsibilities in California and we’ll certainly work with him regarding scheduling should that issue arise,” convention spokeswoman Melissa Subbotin said.

She declined to say whether organizers were considering another option: a Schwarzenegger appearance by satellite from Sacramento, as Republican Gov. Pete Wilson did in 1992 during a similar budget stalemate.