LOS ANGELES — Gov. Jerry Brown of California and the Democratic-controlled Legislature have reached a tentative deal on the state budget, relying on more optimistic revenue predictions to add $4 billion to next year’s budget. The plan, which the Legislature is expected to begin approving on Tuesday, would also trigger deeper cuts in education and social services if those revenues did not materialize.

For months, Mr. Brown, a Democrat, has been cajoling Republicans to support a plan that would ask for voter approval on extending taxes that are scheduled to expire at the end of the month. But he has been unable to secure the four Republican votes he needed for his original plan, which he said would address the long-term deficit the state faces.

The governor said that after months of negotiating with Republicans, “there is an almost religious reluctance to deal with the state budget in a way that requires increased revenue.”