About a million of California's poorest undocumented immigrants would have access to basic low-cost health care under a plan being pushed at the Capitol.

President Barack Obama's federal health care overhaul excludes undocumented immigrants, but some California leaders want to fill that gap by offering a safety net of primary and preventive care that does not consider immigration status.

The county-run program would give undocumented immigrants and legal residents who can't afford health insurance but don't qualify for Medi-Cal the ongoing opportunity to see a doctor, get tested and receive treatment before minor health problems become severe.

Funding would come from an estimated $700 million in county savings tied to expansion of the Medi-Cal program.

Senate President Pro Tem Darrell Steinberg said he strongly supports the concept of improved care for undocumented residents, which is pushed by officials of health care, labor and immigrant groups.

"I think that people who are living in this country, working hard and pursuing (citizenship) ought to be able to care for themselves and their loved ones," he said.

Assembly Speaker John A. Prez said he wants to ensure that counties have adequate funds to serve needy residents who lack health insurance but it's premature to comment further until more is known about cost and number of people requiring care.

"There will always be a population that isn't covered and there will always be an impact on counties. We need to make sure counties have the revenues and the resources to address those needs," Prez said.

Gov. Jerry Brown has taken no public position on expanding care to undocumented immigrants, but his budget proposal does not contemplate such a move and the federal government would not subsidize it, said Toby Douglas, director of the state Department of Health Care Services.

The Brown administration is focused instead on overhauling health care in a way that's "affordable and sustainable," Douglas said.

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Some California leaders want low-cost health care for undocumented immigrants