SACRAMENTO — Since taking office in 2011, Gov. Jerry Brown has helped to resolve some of California’s toughest fiscal challenges — mainly huge structural deficits and old, forgotten debts.

But this year he appears ready to take on Mission Impossible — getting Democrats and Republicans to agree to increase the state’s gas tax to fix California’s crumbling roads and bridges.

Hiking the gas tax has always been politically risky, especially in a state where cars are still king and that -gave birth to the anti-tax revolution in the late ’70s.

But hell might be about to freeze over: For the first time in decades, even anti-tax Republicans are open to raising prices at the pump to start cutting into the state’s $59 billion backlog of roadway maintenance.

“We’re talking about taking some difficult votes,” said Sen. Anthony Cannella, R-Ceres, the vice chairman of the Senate Transportation Committee. “We’re going to get one bite at the apple, and I hope we get it right.”

Brown had telegraphed his intention to take up the issue in his January inaugural address when he asked Democrats and Republicans to do the “impossible” and craft an agreement to improve transportation infrastructure.

“There are many things voters appreciate that aren’t sexy, and this is one of them,” said David McCuan, a political expert at Sonoma State University. “Brown knows we’ve got to get this done.”

As the condition of the pavement worsens and the price to repair it grows, ideas that seemed outlandish a few years ago are back on the table, including a plan by a San Jose lawmaker that would raise vehicle license and registration fees as well as the gas tax.

California’s underfunding of roadway maintenance is nothing new. Over the past decade, the state has used most of its transportation funding on widening roadways — which reduces traffic jams — and road projects that expedite commercial shipping.

But that left little to tackle potholes and other routine repairs.

And as cars become more fuel efficient and many drivers switch to hybrid or electric vehicles, revenue generated by the state’s 48.6-cent gas tax — the backbone of the state’s transportation budget — has dwindled. Current gas tax revenue covers only a quarter of the state’s annual highway repair needs. And the gas tax — now the second highest in the nation, after Pennsylvania — is set to go down 6 cents in July.

Since hybrid and electric vehicle owners pay little to nothing for their use of the state’s roadways, some have suggested charging them a fee for each mile they drive. So far, the idea hasn’t gotten much traction because it raises tough questions about how to track miles driven without invading a driver’s privacy.

If California does end up hiking the gas tax, it would join 18 other states and the District of Columbia that have done so since 2012. Most of those states are controlled by Republicans.

Ironically, bright-blue California is among only a handful of states that haven’t raised gas taxes since the early 1990s.

Waiting any longer to address an ever-growing backlog of roadway repairs will put drivers at risk and cost more in the end, said Sen. Jim Beall, D-San Jose.

That’s why he introduced Senate Bill 16, which seeks to raise at least $3 billion annually for transportation.

“This is an urgent crisis that we have to deal with now,” said Beall, chairman of the Senate Transportation Committee. “If we don’t, we’re leaving the next generation an astoundingly expensive problem.”

Beall’s bill would boost the gas tax by 10 cents per gallon, increase the vehicle license fee by 0.07 percent annually each of the next five years, raise the vehicle registration fee by $35 and start charging owners of electric cars and other zero-emission vehicles $100 annually. Most of the money would fund repairs on state roadways, but some would go directly to cities and counties.

His plan would also return the $1 billion generated annually in truck weight fees to the transportation budget — an idea first proposed by Assembly Speaker Toni Atkins in a February speech to the California Trucking Association. The money currently goes into the general fund.

Much like the cost of the state’s unfunded pension liabilities, the cost of roadway maintenance grows exponentially each year the problems are ignored.

The American Public Works Association estimates that every $1 spent to keep a road in good condition avoids $6 to $14 needed later to rebuild that road once it has deteriorated beyond repair.

“It’s like we’re at the top of a waterfall, and we need someone to throw us a life preserver to pull us back from the precipice,” Beall said. “If we don’t catch the raft, we’re going to go down really, really fast.”

To reach the governor’s desk, Beall’s plan must win approval from two-thirds of lawmakers in both the Assembly and the Senate. He’ll need GOP support now that the Democrats have lost their supermajorities in both houses.

Asking Republicans to raise taxes and fees is almost always a tall order, but Senate GOP leader Bob Huff, R-Diamond Bar, said his caucus is also interested in tackling deferred roadway maintenance this year. He called Beall’s plan a “creative” solution to a vexing problem.

A coalition of anti-tax Republicans who oppose the bill will likely form this summer, but so far Beall’s bill has been through two committees and it’s drawn only two “no” votes from Republicans, although many have abstained.

Last month, Senate Republicans introduced Senate Constitutional Amendment 7, which mirrors parts of Beall’s plan and seeks to close the loophole in current law that allowed truck weight fees to be diverted to the general fund in the first place. But even Huff said the measure doesn’t go far enough.

“There are some in our caucus who would vote for a more robust transportation package,” Huff said. “A clean, clear nexus between what’s being raised and how the money is being spent is the magic formula for winning Republican support on this.”

Anti-tax groups are sure to oppose any effort to raise taxes or fees, but California shouldn’t have to wait any longer for lawmakers to address the road problem, said Will Kempton, executive director of the California Transportation Commission.

A well-maintained network of roads, he said, is vital to the state’s economy and quality of life.

“Any time you can’t get goods to market in a reasonable amount of time, productivity suffers,” Kempton said. “And think of all the people trying to get home to catch a soccer game who can’t because they’re stuck in traffic. We need a solution.”

Contact Jessica Calefati at 916-441-2101. Follow her at Twitter.com/Calefati.