Efforts to expand health care coverage for people in New York without immigration status are likely at a standstill after Gov. Kathy Hochul doubled down on her concerns Tuesday about the cost of the proposal.

Members of the state Assembly remain focused on legislation that passed the Senate during a two-day special session in Albany this week, but chances of a measure passing to expand health care coverage for thousands of undocumented New Yorkers is growing slim.

The bill, called Coverage For All, would direct the state health commissioner to request a waiver from the federal government to allow undocumented people to enroll in the state program and use a surplus of federal funds to pay for that expansion for New Yorkers not typically covered in the state's Essential Plan under the federal Affordable Care Act. 

"It would expand eligibility for New York state residents who meet the income requirements to enroll in health care," sponsor Assemblywoman Jessica González-Rojas said Tuesday.

Advocates have increased their pressure on the Assembly to vote to pass the bill while in Albany this week. Democratic U.S. Rep. Jamaal Bowman released a video on Twitter on Tuesday night to urge the Legislature to pass the bill and send it to Gov. Hochul's desk.

If it became law, the measure would expand coverage for an estimated 240,000 people New Yorkers. It would cost about $1.2 billion for coverage if all of enrolled in the program. 

But Gov. Hochul reiterated her fiscal concerns about expanding the state's Essential Plan under the federal Affordable Care Act during an event about statewide efforts to reduce gun violence late Tuesday morning as Assemblymembers conference.

She warned the state must err on the side of fiscal caution after a recent state comptroller report shows the state took in $6 billion less in tax revenue than expected.

"I also have to be cognizant of the extraordinary cost that would be imposed on New York state taxpayers at a time when the warnings about our finances are troubling," Hochul said. "We cannot ignore those, we have to make sure that we manage our finances as well."

The governor's concerns indicate she would likely veto the measure if it came to her desk for a signature. 

González-Rojas says the governor's statements are misleading because the estimated $1.2 billion would come from the federal government, and it would save the state more than $500 million in annual emergency Medicaid expenses already spent to cover services for undocumented people.

"That cost will be borne by the federal government and not the state government," she said. "We will not use state dollars for this program."

Last year, Hochul said she expanded health care coverage for undocumented senior citizens and for postpartum mothers in the first year of their child's life.

"The federal government has told us we cannot use the trust fund money that's available that's in surplus right now," Hochul said. "We cannot use that for undocumented individuals. So we've been having conversations, but I know the Assembly is looking at it."

Senate sponsor Sen. Gustavo Rivera, a Bronx Democrat, received a letter from the U.S. Department of Health and Human Services earlier this month detailing how the waiver could legally be used to fund state subsidies for health coverage "for people who are not lawfully present," who are otherwise ineligible for coverage.

The law was recently amended to include guardrails to allow the state health commissioner to slowly roll out the program, or cap it if necessary.

But lawmakers will continue to discuss the bill in conference, giving supporters hope.

"It's sitting in Ways and Means [Committee]," González-Rojas said. "We're hopeful it will get a vote within the next two days."

The push for the legislation is unrelated to the recent increase of migrants arriving in the state to seek asylum. Asylum seekers have a federally recognized immigration status, which permits them to enroll in Medicaid or the state's Essential Plan health care program.