MARTINEZ -- A divided Contra Costa County board of supervisors is commissioning a poll gauging voter support for a countywide sales tax hike to fund a growing menu of public safety and public health-related services in the wake of the announcement that Doctors Medical Center San Pablo will likely close.

The tax idea, for an extra quarter-cent or half-cent on the dollar, emerged after the May 6 defeat of Measure C, a parcel tax in the West Contra Costa Healthcare District designed to plug an $18 million-a-year operating deficit and avert the closure of the hospital and its emergency department.

A new quarter-cent sales tax hike could raise $38 million a year, and a half-cent hike could raise $76 million, according to county estimates.

Proponents of saving the hospital noted that Alameda County voters passed a half-cent, special health care tax in 2004. Voters Tuesday extended the tax until 2034.

The poll proposed by supervisors John Gioia and board Chairwoman Karen Mitchoff at Tuesday's board meeting would gauge voter preference and support for a broader sales tax geared to "public safety, emergency response, health care services, and other critical needs in Contra Costa County."

Gioia said Thursday the idea of such a tax has been kicked around for some time, but the threatened closure of the hospital, coupled with the Aug. 8 deadline to put a tax measure on the November ballot, contributed to the timing of the poll.

Gioia, Mitchoff and Federal Glover voted in favor of the poll, which would cost up to $45,000. Candace Andersen and Mary Piepho opposed it.

The broad range of funding applications aims to qualify the tax as a general tax requiring a simple majority vote, as opposed to a specified-use special tax requiring a two-thirds majority, such as Measure C. That measure collected only 52 percent yes-votes, far short of the required 66.7 percent.

On Tuesday, Gioia singled out the importance of the hospital's emergency room among other reasons to support a tax. Mitchoff talked about hiring more sheriff's deputies, opening fire houses, and even supporting library services, in addition to public health.

Glover said the scope of the proposed tax was "too broad," and suggested it be refined. He also said he does not want the proposed tax to be looked at as "a bailout" of Doctors hospital.

Andersen noted that the county already spends about $30 million a year from the general fund on the county hospital in Martinez, and said Doctors needs to come up with a new business model. She also questioned whether a tax would bring any benefit to her district.

Piepho, criticizing what she perceived as a rush to impose a county tax, suggested working on the federal level to increase Medi-Cal and Medicare payments.

"The taxpayers are fatigued," Piepho said.

Advocates speaking at Tuesday's meeting mostly cited public health, and in particular Doctors hospital, as the primary reason to support a tax. Several speakers warned that eliminating more than half of West County's emergency beds would wreak havoc on the countywide emergency medical system and endanger lives.

Doctors hospital has 25 of the 40 emergency beds in West Contra Costa, out of a countywide total of 267.

Firefighters Local 1230 President Vince Wells spoke in favor of a poll to find out what services voters think are important.

Alex Aliferis, executive director of the Contra Costa Taxpayers Association, questioned whether tax proceeds would be used to pay down unfunded pension liabilities.

Contact Tom Lochner at 510-262-2760. Follow him at Twitter.com/tomlochner.