Clobbered by state cuts and operating on the brink of financial peril, Boston Medical Center has been burning through some $12 million a month out of its reserves to keep going.

Meanwhile, employees are agitating for more of a voice in future service or jobs cuts.

Already, some 1,000 Boston Medical Center workers have signed a petition calling for a greater employee role at the decision-making table. The signers include doctors, nurses and members of SEIU 1999, a health-care workers union.

On Tuesday, workers hand-delivered the petition to the office of Elaine Ullian, the medical center’s embattled chief executive.

“We take our management role seriously and none of our decisions have been made lightly,” said hospital spokeswoman Ellen Berlin. “While we continue to talk to our unions and listen to their feedback, it is management’s role to make decisions about the best and most efficient ways to deploy hospital resources.”

The petition was just the latest salvo in an increasingly tense situation.

Just before the center began shedding jobs and curtailing operations, Ullian took home a $3.5 million bonus, on top of her $1.3 million salary.

This past summer, the medical center, which treats the region’s poorest people, sued the state, saying it had reneged on promised reimbursement rates for health care.

Berlin confirmed that the medical center has been regularly tapping into its $189 million reserve fund to pay for operations.