LOS ANGELES — By this point in his tenure, Gov. Jerry Brown had hoped to have dispensed with the huge budget shortfalls that greeted him when he took office. Yet on Monday, there was Mr. Brown in a familiar, if uncomfortable, position: calling for severe spending cuts, this time to deal with a new $15.7 billion shortfall.

Mr. Brown’s campaign to persuade voters in California, the birthplace of the antitax movement, to vote for tax increases to head off even more cuts seemed at one point to have a good chance of winning. But now it is threatened by a rival tax plan that went onto the ballot after Mr. Brown was unable to persuade its organizers to stand down.

And what is perhaps the most prominent nonbudgetary initiative on Mr. Brown’s docket — a high-speed rail line to whisk riders between San Francisco and Los Angeles, the kind of legacy project identified with his father, Gov. Pat Brown — is embattled as well, facing rising opposition and questions about its feasibility and cost.

These are not easy days for Mr. Brown, a Democrat, as he approaches the midpoint of his term. The promises of his election — to end partisan wrangling, to deal with budget problems that have hamstrung the government of the world’s ninth-largest economy, to establish his own legacy as he approaches the end of his career — have to date been largely frustrated. After a long and varied career in public life, Mr. Brown, 74, finds himself stymied by a governing system that seems impervious to his considerable skills and a budget that defies his vision of the state as a sunny engine of continued growth and reinvention.