The Republican governor said lawmakers were willing to cut $10 billion from education but are reluctant to trim just $1.2 billion from prisons.
"They don't have the guts to go out there and create the prison reform that they have been talking about now for two decades," he said. "They (Assembly members) don't have the guts now to make those decisions, because they are now more worried about safe seats than safe streets."
He made the comments Wednesday in an online conversation with the founders of Twitter at the company's San Francisco headquarters.
"The governor should spend less time sending provocative tweets and more time producing Republican votes," retorted Shannon Murphy, spokeswoman for Assembly Speaker Karen Bass, a Democrat from Los Angeles.
Hours later, the Assembly again postponed a prisons vote that had been set for Thursday, pushing the debate into next week.
Assembly Minority Leader Sam Blakeslee took personal offense at the governor's remarks.
"I'm concerned about those who don't have the spine to stand up for public safety," said the Republican from San Luis Obispo.
"Early release and a sentencing commission would produce the greatest legislative risk to public safety seen in a generation," he said. "We're proud that we stood strong and ensured those risks did not pass last week."
Schwarzenegger is proposing to reduce the prison population by 27,000 inmates in the first year by diverting thousands of criminals to local jails or home confinement.
Bass says the plan can't win support among her Democrats, and Republicans adamantly oppose provisions they say amount to early inmate release.
Bass plans a vote Thursday on an alternative that would leave the state with a new $200 million budget hole.
The debate is a holdover from last month, when lawmakers of both parties agreed to cut the corrections budget by $1.2 billion to help bridge a massive budget deficit. But lawmakers delayed a vote on the details.
Schwarzenegger praised Democratic state senators, who approved a broader prison bill last week that would close the entire budget gap.
"They have made great decisions," Schwarzenegger said. "The Assembly still has a big problem with that and so we are pushing them to come to a good conclusion."
Bass' alternative would strip out the most controversial provisions. Those include lowering sentences for certain crimes, sending those offenders to county jails instead of state prisons. She also rejected allowing home detention with electronic monitoring for inmates with less than 12 months to serve, who are over age 60 or who are medically incapacitated.
She plans a separate vote on a bill that would create a powerful commission to review criminal sentences. Law enforcement organizations and Republicans strongly oppose the commission because its recommendations would take effect automatically unless they were rejected by both chambers of the Legislature.