LOS ANGELES — Ever since he came into office, Gov. Jerry Brown has promised to address what he has long called the state’s “wall of debt” built up over years. And now that the nation’s most populous state is looking at a multibillion-dollar surplus, Mr. Brown, in a $155 billion state budget proposal submitted on Thursday, is pledging to make good on that promise.

While Mr. Brown called for an 8.5 percent spending increase, he also proposed spending $11 billion on debts and liabilities, including a $6 billion deferred payment to schools and roughly $4 billion to pay down economic recovery bonds issued by his predecessor, Gov. Arnold Schwarzenegger.

Mr. Brown’s budget was missing some of the proposals for new spending on social programs, like universal prekindergarten, that many Democrats have called for.

Some Republicans quickly praised Mr. Brown’s approach, but it could set off a fight among fellow Democrats, who control the legislature and hope to use some of the projected $4.2 billion surplus to restore program cuts.