At the same time, health insurance experts warned that the administration's decision to end those federal payments will tend to financially harm middle-class Obamacare customers and comes at perhaps the worst possible time to take such an action.
"This is an effort to blow up the system," said Schneiderman. He accused Trump of lashing out in frustration over the inability of Republican allies in Congress to pass a bill that would repeal and replace Obamacare.
"We're not going to let him do it."
"We will be in court to defend these subsidies and fight this decision with everything we've got," Schneiderman said as he announced the lawsuit.
California Attorney General Xavier Becerra said that in addition to his state and New York, 15 other states and the District of Columbia will be filing suit in federal court in the Northern District of California.
"In one week, the Trump Administration has re-opened the door to 'junk' health insurance plans and cut off access to contraception for millions of women," said Becerra.
"Now they're refusing to comply with federal law in a way that will hike the cost of care for millions of Americans by withholding critical subsidies that make care more affordable."
The suit will be based on the claim that the Affordable Care Act "is the law of the land," and the cost-sharing reduction payments are "a critical part of the ACA," Schneiderman said.
"They must be preserved as an integral part of this system," said Schneiderman.
The Trump administration Thursday night said it would stop paying billions of dollars worth of reimbursements to health insurers to compensate them for out-of-pocket health discounts given to 6 million Obamacare customers.
Those customers, who earn between about $12,000 and $29,700 annually, pay less for co-payments, coinsurance and deductibles when they obtain medical services and prescription drugs, as a result of the CSRs.
The administration said its move was necessary because Congress never authorized those payments, which have been made to insurers for years.
Eric Hargan, acting secretary of the U.S. Health and Human Services Department, and Centers for Medicare and Medicaid Services Administrator Seema Verma in a joint statement said, "It has been clear for many years that Obamacare is bad policy. It is also bad law."
"The Obama Administration unfortunately went ahead and made CSR payments to insurance companies after requesting — but never ultimately receiving — an appropriation from Congress as required by law."
But Schneiderman said that argument is akin to selling someone a car but saying that the wheels have to be paid for separately. He said the ACA itself authorizes those reimbursements.
However, unless legal or legislative action blocks the move, the decision to cut off the cost-sharing reimbursements is expected by the Congressional Budget Office to lead to premiums that are 20 percent higher than they otherwise would have been in 2018. That is because insurers will still have to offer the CSR discounts to their low-income customers, despite the loss of the federal offset money.
By 2020, individual health plan premiums are expected by the CBO to be 25 percent higher.
Insurers in dozens of states already had adjusted their proposed rates for 2018 in anticipation that the CSR reimbursements could be cut off.
"I think every citizen should be outraged," former U.S. Health and Human Services Department Secretary Kathleen Sebelius told CNBC about the decision to cut the CSR reimbursement.
"We're not playing a game here. This is really people's lives ... we're talking about your health, your kids' health and your parents' health," said Sebelius, who oversaw implementation of the Affordable Care Act for the Obama administration.
"I think there's no question it will cause some insurers to rethink, potentially, being in the market at all, and it causes huge rate increases," Sebelius said.
She said that "in the 19 reddest states" — those Republican-leaning states that most strongly supported Trump in the presidential election — "you will have the biggest cost increases."
That is because those states as a rule did not expand Medicaid under the ACA, which means that more low-income people buy Obamacare plans and get CSR discounts in those plans.
However, not everyone will have to foot those higher premium bills. More than 80 percent of people who buy Obamacare plans on government-run marketplaces such as HealthCare.gov qualify, by virtue of their low or moderate incomes, for federal subsidies that reduce the amount they have to pay for their premiums.
Because those subsidies, in the form of tax credits, increase in value as premiums rise, most or all of the increases in premiums due to the end of CSR reimbursements will not have to be paid for by subsidized customers.
Sebelius said that the people who will be hit with the full effect of the extra premium hikes will be customers of Obamacare exchanges who earn above 400 percent of the federal poverty line, or nearly $100,000 annually for a family of four. No one who makes over 400 percent of the poverty level qualifies for premium subsidies.
She also said everyone who buys individual health plans outside of those Obamacare exchanges, such as through a broker or directly from an insurer, will have to pay all of the higher premiums that result from the CSR cutoffs. That is because the premium subsidies are available only to people who buy on the government-run insurance markets.
Robert Laszewski, a health insurance consultant, in an analysis of the Trump decision said that 44 percent of the customers in Obamacare-compliant plans in the individual health insurance market did not get a subsidy in 2017.
That equals "6.7 million out of a total Obamacare compliant individual market of 15.4 million," Laszewski wrote.
Gary Claxton, an Obamacare expert with the Kaiser Family Foundation, said that if the CSRs are cut off permanently "in the long run this [Obamacare] isn't going to keep up."
Claxton said that while lower-income Obamacare customers would be insulated from the premium hikes, higher income people would not, creating a two-tier system that would not be acceptable politically.
"It's got to morph into a different system in the long run," Claxton said.
He noted that "the premiums in some of the rural areas [of the United States] in particular are already high."
Claxton said Trump has picked close to the worst possible time to kill the subsidies.
Open enrollment in Obamacare plans is set to begin Nov. 1. Claxton said the news about the CSR shutoff, as well as about an executive order Trump signed earlier Thursday, which was also designed to undermine Obamacare, "puts all sorts of clouds over the marketplace at a time you might suggest they enroll in coverage."