LOS ANGELES - California has some of the toughest antismoking laws in the country - it is illegal, in some places, to smoke in your own apartment - and boasts the second-lowest per capita smoking rate in the 50 states.

But for all the disdain toward smoking here, it has been 14 years since California raised its cigarette tax, a tribute to the power of the tobacco industry here and the waning of this state’s antitobacco dominance.

That may be about to change. An array of health and anticancer groups has rallied behind a ballot initiative to impose a $1-a-pack cigarette tax to finance cancer research. The current tax of 87 cents is about half the national average and ranks 33rd in the nation.

The move to increase the tax has provoked a $47 million storm of ads, overwhelmingly financed by the tobacco industry, which is outspending proponents by nearly four to one to defeat the biggest threat it has faced in more than a decade.

An independent poll released two weeks ago signaled the power of the assault: While a majority of California voters still say they support Proposition 29, as it is known, the percentage has dropped markedly since the campaign began, according to the Public Policy Institute of California poll. The vote will be held Tuesday.

The latest frontier in the fight against smoking is a very unlikely place: a state that has long been identified with championing restrictions on smoking.

The battle has drawn national attention - Mayor Michael R. Bloomberg of New York contributed $500,000 to the initiative, and Lance Armstrong, the bicycling champion and cancer survivor, has become its chief public advocate - reflecting the frustration of antismoking groups on their defeats here. The Legislature has voted down more than 30 attempts to raise cigarette taxes in 30 years.

“You think of California as a healthy, progressive state leading in tobacco cessation,’’ said Chris Lehman, one of the organizers behind the initiative. “It’s just not. And it’s not for lack of trying.’’

California’s dominance as a leading antismoking state has declined significantly since it passed, in 1998, what was at the time the toughest antismoking bill in the country, according to the American Cancer Society. Since then, 23 states have passed tougher laws. The cancer society has contributed more than $7 million to get Proposition 29 passed.

“California has been a leader, not only in the country but in the world, in efforts to curb smoking,’’ said John R. Seffrin, the chief executive of the society. “They are overdue.’’

The tax, which would raise an estimated $735 million, is being voted on as California is reeling from a new wave of bad budget news. Governor Jerry Brown said last month that the state faces a $16 billion deficit, and proposed a round of severe spending cuts to deal with it.

But none of the $735 million would go to close the deficit. Organizers argued that the tax would have less chance of passing if voters thought it would go into the state coffers, and said their only goal here was cutting down on smoking. Raising the cost of tobacco has proved to be the most effective way of discouraging smoking, particularly among teenagers.