LOS ANGELES — Gov. Jerry Brown jumped up from his desk on the 16th floor of the Ronald Reagan State Office Building the other morning, riled over evidence that his ballot initiative to raise taxes and head off billions in education spending cuts might be headed for a potentially catastrophic defeat.

“This is a measure paid for by relatively few that affects millions of people in this state,” Mr. Brown said, jabbing the air with a pen. “It is hugely important to this state: The idea of what it is should carry it to victory. Just that.”

Perhaps. But with two days until Election Day, Mr. Brown’s proposition is struggling, raising the prospect of as much as $6 billion in new cuts to California’s already battered public education system. It also is emerging as a serious challenge to Mr. Brown, who has affixed his personal prestige to its passage. The outcome holds the potential to hobble a governor whose hoped-for legacy had been wresting California from a fiscal crisis.

Three recent polls have shown Proposition 30, as it is known, declining in support since earlier this year. Now, barely 50 percent of likely voters said they planned to vote for it; historically, tax initiatives tend to fail if they fall below 50 percent this close to an election.