Access to basic health care. That's what Medicaid delivers for more than 3 million New Yorkers enrolled in the program.

"More and more, it's not just the emergency room. It's primary care. It's when a mom needs to take her kid to a pediatrician," de Blasio told reporters this week during his annual preliminary budget briefing.

The city is gearing up for the possibility of budget cuts as Albany struggles to close a $6 billion dollar gap, $4 billion of which is due to the rapid rising cost of Medicaid and a massive increase in enrollment.

New York is somewhat unique in how it handles Medicaid costs. Localities are required to make a contribution, where other states typically split the cost between the federal government and the state government. The money then flows to managed care companies, hospitals, nursing homes, doctors, and other medical service providers who service 3.4 million New Yorkers across the five boroughs.

Steve Banks, Commissioner of the New York City Human Resources Administration and the Department of Social Services, said Medicaid provides a health care safety net for some of the most vulnerable New Yorkers.

"Children, there are newborns, there are toddlers, there are teenagers, there are senior citizens, there are hard-working people who are working, you know, low-wage jobs," Banks said.

For years, the city has been contributing a maximum of $5.9 billion per year to meet its requirement. The number is capped, allowing the city to budget for it every year.

"It's a statewide program, so there are state standards that are set and the localities, whether it's New York City or some other part of the state doesn't make determinations about what should be the eligibility standard," Banks said.

But now, the state is looking to New York City and other localities to make up the difference, saying it's time they pay for a program they help to run.

George Sweeting, deputy director at the Independent Budget Office, said the state is now in financial straits as a result of rising costs.

"What's happening now is that state has a much-larger-than-anticipated deficit," Sweeting said.

Then, there is the issue of an accounting maneuver by the state.

"The state made it worse for itself by not paying $1.7 billion that was actually due in the prior fiscal year. They delayed the payment enough. All that does is delay the problem," he said.

And while de Blasio raised alarms this week about the impact cuts could have, city officials are hopeful a resolution will be found in negotiations over the coming months.

"Nothing has changed. The state is putting out a budget next week that will have proposals. We're going to do everything we can to make sure that no one loses their services or their health care," Banks said.

City officials will get their first look at the numbers next week, when the governor releases his annual budget briefing. It's scheduled for Tuesday.