Sylvia Burwell also said the president would reject any proposals restoring those subsidies that Republican lawmakers have already produced because all would roll back crucial elements of the overhaul law, in effect repealing it.
"Something that repeals the Affordable Care Act is something the president will not sign," she said.
Burwell's comments to the House Ways and Means Committee marked a continuation of Obama administration efforts to pressure Republicans should the justices void subsidies that help millions afford health insurance. A decision is expected this month.
The GOP runs Congress, and 26 of the 34 states likely to be hardest hit by such a decision have Republican governors.
In addition, 22 of the 24 GOP senators up for re-election next year are from those same 34 states. Many Republican strategists have said the party would face retribution from voters in next year's elections if the subsidies are eliminated and Congress does not advance legislation protecting the millions of people who would be hurt.
The case before the Supreme Court involves a Republican-backed challenge by conservatives to the 5-year-old health law. The suit says the law limits the subsidies to people in states that run their own insurance marketplaces — and not to residents of the 30-plus states that use the federal HealthCare.gov website.
The committee chairman, Rep. Paul Ryan, R-Wis., asked Burwell how the administration would respond to a decision that tossed out the subsidies.
"We're going to do everything we can and we're working to make sure we're ready to communicate and work with states," responded the health and human services secretary.
But she added, "The critical decisions will sit with Congress and states and governors to determine if those subsidies are available."
Burwell's comments were a more pointed version of previous administration statements that it is not preparing a contingency plan for a decision that erases the subsidies, which are paid as tax credits.
Though many Republicans seem to favor extending the federal aid temporarily, none seem ready to back down from demands that in exchange, other parts of the health law should be jettisoned, such as its requirements that insurers provide minimal levels of coverage.
The day's back and forth showed that the law remains a high-octane political issue destined to influence next year's presidential and congressional elections.
"They still refuse to entertain the notion that their health care law might get struck down by the Supreme Court," Ryan told reporters afterward. "And they refuse to acknowledge they are even thinking about a backup plan. I think that's unfortunate."
While Ryan said the health law "is busted," Rep. Sander Levin of Michigan, the top Democrat on the committee, said the only thing broken is the GOP attack line on the law.
"You sit as armchair critics as millions of people have insurance who never had it before," Levin said. "You're livid because it's getting better?"
Congressional Republicans have worked on several plans to temporarily restore the credits and curb some of the law's requirements, though there are no signs that any have enough votes to win approval. Republicans say they hope to come out with a plan backed by both House and Senate GOP leaders once the court strikes down the subsidies.
One bill, from Sen. Ron Johnson, R-Wis., who faces a tough re-election fight next year, would extend the credits until August 2017 while erasing the requirements that individuals buy insurance and that employers provide coverage to workers. It has 31 co-sponsors, including Senate Majority Leader Mitch McConnell, R-Ky.
"That piece of legislation, from our perspective, is repeal" and Obama would not sign it, Burwell told the committee.
Republicans hope a Republican in the White House in 2017 would help them repeal Obama's law and replace it with one that has fewer strictures.
In the 34 states most likely to feel the brunt of a court decision annulling the subsidies, 7.3 million people have used HealthCare.gov to register for coverage and made initial payments.
About 88 percent of them — 6.4 million people — receive federal subsidies averaging $272 monthly. Experts say many of them would drop their coverage if the subsidies disappear because losing the assistance would make their insurance unaffordable.