About two million New Yorkers have signed up for insurance under the Affordable Care Act, with three out of every four of them poor enough to qualify for Medicaid, according to figures released Wednesday by the Cuomo administration.

While Gov. Andrew M. Cuomo heralded the overall numbers as a sign of the success of the program, having such a large proportion on Medicaid, which is funded by the government, could impose a heavy new burden on public finances.

But insurance experts said they expected the impact of the new Medicaid enrollment to be mitigated by the greater access to health care. In other words, they said, having Medicaid coverage would give people access to primary care that could keep them from developing a chronic disease or becoming catastrophically sick and ultimately costing the system even more.

“Theoretically, could these numbers of people eventually push that Medicaid number up higher? Yes,” James R. Tallon Jr., president of the United Hospital Fund, said on Wednesday.

But, he added: “Having most people insured is the key to controlling long-term cost growth because it means you can manage care in a more effective way.”

By and large, experts said, those signing up for private insurance on the state’s Affordable Care Act health exchange are people who were priced out of the market before. The law raised the income ceiling for Medicaid eligibility in New York and other states that accepted the expansion of the program; a family of four can now earn about $33,000 and still qualify. Many people who earn too much for Medicaid can get subsidies to help them buy private insurance.

Though Republicans in Congress have criticized the public costs and tried several times to repeal the law, which was passed in 2010, President Obama has vowed to veto any attempt to overturn it.

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Jeffrey R. Ungvary President