But the obstacles are considerable. California gas prices are spiking, as they do each summer as the state switches to a lower-pollution — but more expensive — blend. The average price for regular gasoline is $3.66 a gallon in California, far above the national average of $2.80, according to figures compiled by the AAA.

Mr. Brown just signed his final budget, which projects a $6.1 billion surplus, money that Republicans are arguing should be used for road repairs, eliminating the need for a gas tax that forces Californians to pay more at the pump.

California Republicans have seized on the issue. Taxes have long been a point of divisions between Republicans and Democrats, and all the more so since Mr. Trump and congressional Republicans enacted a tax reform bill that severely reduced deductions for state and local taxes, posing a particular burden for California homeowners. Kevin McCarthy, a California Republican who is the House majority leader and looking to become its next speaker, has contributed money to the repeal in an effort to save seven Republican congressional seats.

Mr. Cox said he had found a “ton of support” for the repeal.

“Whenever I am out campaigning, I always talk to working people — valet parking people, the desk clerks, the people behind the counter,” he said. “I ask people what do they think about the cost of living and the gas tax. And they say: ‘We can’t take this. We had to move an extra 20 miles away because we couldn’t find an apartment we could afford. And now we are sitting in traffic burning up gasoline at almost $5 a gallon.’”

“Mr. Brown and Mr. Newsom are being dishonest when they say these projects will come to a halt if we don’t have this tax,” he said. “They know that these road projects could be done if we changed work rules, if we used money more efficiently, if we cut better deals to make the process more efficiently.”

A U.S.C. Dornsife/Los Angeles Times poll in May found 38 percent of voters said they supported the gas tax, a perilously low number; only 49 percent of Democrats said they supported it. Backers of the initiative gathered over 900,000 signatures to get it on the ballot; only 585,407 were needed.