The vote was 51-16; with 13 members abstaining, before the Assembly adjourned.
The bill failed to get the required two thirds majority after Roger Niello, R- Fair Oaks, urged fellow members of the legislature to either vote against it or abstain from voting.
Niello said the Assembly should not pass the bill until after the May 19 special election, when California voters weigh six ballot propositions to deal with the state's budget gap.
A spokesman for Assembly Majority Leader Alberto Torrico, D-Newark, said AB-964 remains on file, and will eventually be brought back for another vote. When is unclear.
Niello appears to be using Republican clout to offer the governor some leverage - holding out on the contract approval as long as possible so that the SEIU doesn't mount a major attack-ad campaign on propositions he favors, such as 1A.
That proposition would give the governor new power to unilaterally make mid-year cuts in spending to some programs and extend certain tax increases by two years.