WASHINGTON — President Trump told a group of governors on Monday that he was pulling back from efforts to repeal the Affordable Care Act, reasoning that with the end of the individual mandate already in force, the law was basically “not Obamacare anymore.”

About an hour later, the White House released a budget proposal for the fiscal year that begins in October, and it was not quite as casual about the current state of health care affairs.

While the budget failed to detail an alternative to the Affordable Care Act, it did include a very specific savings target that would entail significant changes: $844 billion in cuts over a decade to execute what the budget called the “president’s health care vision.”

“While Americans have the best health care options in the world, rising health care costs continue to be a top financial concern for many Americans,” the document read. “The president’s great health care vision will ensure better care at lower costs.”

Mr. Trump is running for re-election this year, so his budget can be read as a policy blueprint for his second term if he wins. The budget leaves to the imagination just what that vision is. Unlike in previous years, when the health care budget laid out specific plans to repeal large sections of the Affordable Care Act and replace it, this year’s proposal barely mentions President Barack Obama’s signature health care law.

But the deep cuts enshrined in the budget’s numbers are not consistent with modest tweaks. Taken together with Medicaid changes recommended elsewhere in the budget, the proposal would strip about $1 trillion out of Medicaid and the Affordable Care Act’s premium subsidies, the two pillars of the law’s expansion of insurance coverage. By 2029, the cuts to those programs in Mr. Trump’s budget would represent around 85 percent of the total that the Congressional Budget Office estimates would otherwise be spent on Obamacare coverage that year.

Aviva Aron-Dine, the vice president of health policy at the progressive Center on Budget and Policy Priorities and a former Obama administration budget and health care official, said that she found the magnitude of cuts difficult to square with the budget’s language.

“You can’t cut $1 trillion from these programs and protect the most vulnerable,” she said.

Mr. Trump began his presidency with a promise to repeal the Affordable Care Act, but efforts to do so in 2017 were unsuccessful. Despite Republican control of both houses of Congress, legislators were unable to agree on an approach. The Senate tried and failed to pass several different bills that would have reshaped big parts of the 2010 health law.

With Democrats making health care central to their 2020 campaigns, Mr. Trump has been facing pressure to propose his own health care overhaul. He has repeatedly promised to release one. The administration is backing legal action pressing to declare the entire health law unconstitutional, and if it wins in court, the result could be a wave of disruption as an estimated 20 million Americans lose health insurance, insurance consumer protections crumble, drug approval pathways disappear, and Medicare fraud statutes are weakened, among many other effects.

Mr. Trump’s budget gives no indication of how he would ameliorate such repercussions.

The budget does stick more closely to another Trump campaign promise: to leave intact the Medicare program for Americans over 65. Though the budget does propose reducing program spending by around half a trillion dollars through a series of cuts to payment policies, it does not make any major changes to the benefit structure of the program or for the populations that will be eligible for coverage.

In some ways, the Obamacare lawsuit is a bigger threat to Mr. Trump’s Medicare promises than the budget: If the White House wins in court, Americans over 65 would have to pay more for prescription drugs because the health law includes a significant provision for Medicare drug coverage. A repeal would also deplete the Medicare trust fund much more quickly.

In previous budgets, the White House’s official position on replacing the Affordable Care Act was a legislative proposal co-sponsored by Senators Bill Cassidy of Louisiana and Lindsey Graham of South Carolina, both Republicans. That plan would have replaced income-based funding for health insurance to one in which states were given blocks of money to spend largely as they wished. That proposal would have also resulted in major reductions in federal spending over time. This year, the budget’s cuts are just as big; they are just far more vague.