Budget talks continue this afternoon at the Capitol, as Governor Schwarzenegger attempts to stake out what sounds like a middle ground over the issue of government funded health care for children who are illegal immigrants.

Yesterday, there was a lot of discussion about a Democratic proposal to expand the number of kids eligible for the state’s Healthy Families program– and more specifically, how some of those kids would be ones who are in California without legal status.

Republican legislators have been balking at medical coverage for those children, while Democrats criticized the standoff as having to do more with the politics of immigration than the state budget.

At a news conference this morning, I asked the governor where he came down on the issue. His initial answer was all about the cost of the proposal.

“We cannot afford that yet,” said Schwarzenegger. “I will not go in the direction of expanding the Healthy Family [sic] program, because we cannot afford it.” He said the state could only afford to offer coverage to the children who are already eligible, based on their family’s income.

But I followed up by asking him to address the broader philosophical issue being raised by his fellow Republicans. And here, Schwarzenegger sounded a little critical of some of this week’s rhetoric.

“For me, we should not politicize the children,” he said. But then, he went further. “Every child, if they are here legally or illegally, every child should have the right to some health care and to schooling. That’s where I’m coming from.”

Chances are that’s a middle ground that will leave some on both sides grumbling. Democrats say the amount of money in dispute is small potatoes compared in a $100+ billion budget. Republicans, however, have been quoted as saying illegal immigration health care is a deal breaker on the budget.

And all sides may wish they could just wait until this November– when voters will weigh a ballot initiative that would fully pay for the health care program (and other health needs) through a new tobacco tax.