More than 6 million Southern Californian households could pay $3 more a month to help cover the costs of Gov. Jerry Brown’s controversial plan to bore two huge tunnels under the Sacramento-San Joaquin Delta.

But that’s cheaper than the $5 a month that households in the Metropolitan Water District of Southern California’s service area were expected to pay under projections released four years ago, Jeffrey Kightlinger, the water district’s general manager, said Thursday.

“Given the importance of this project to maintain water supply…