Californians who use debit cards to pay for goods and services could not be charged a fee by stores and other retail outlets under legislation sent Thursday to Gov. Arnold Schwarzenegger.

Democrats succeeded in pushing Senate Bill 933 through the Assembly by the bare minimum number of votes necessary, 41-22, with support from only six Republicans.

Proposed by Sen. Jenny Oropeza, D-Long Beach, the bill would include debit cards in an existing prohibition barring retailers from charging a fee on transactions paid with credit cards.

"The issue is simple fairness," Oropeza said in a written statement about SB 933.

"As it now stands, retailer-imposed checkout fees on top of advertised sticker prices are costing consumers hundreds of millions of dollars. This is hitting lower-income families the hardest, especially those using government-issued cards," she said.

Opponents characterize the bill as harmful to small businesses because it addresses only one side of debit-card fees: It does nothing to bar the issuers of ATM cards from charging retailers when customers use them.