CHICAGO — Throughout the country, relief was the dominant emotion among consumers who get help from the government to lower their health insurance costs following Thursday’s Supreme Court ruling upholding the subsidies underpinning President Barack Obama’s health care overhaul.

Many consumers expressed somewhat conflicting views: They were happy their monthly premiums would continue to be affordable but exasperated by the coverage the policies purchased on the new health care exchanges provide.

“I don’t particularly care for Obama. I didn’t vote for him,” said Salt Lake City resident Paige Preece, whose subsidy allows her to buy insurance for $137 a month. “But, honestly, if it weren’t for this, I would be absolutely lost.”

The court’s 6-3 ruling upheld the federal financial assistance to millions of low- and middle-income Americans to help pay for insurance premiums regardless of where they live. An estimated 6.4 million people in the 34 states that used the federal health care exchange were at risk of losing the subsidies because their home states did not set up their own insurance exchanges.

The case turned on just a few words in the mammoth Affordable Care Act that suggested the federal subsidies could go only to consumers in states that operated their own health insurance marketplaces. Consumers in those states or in ones that fell back on the federal exchange when their own exchanges faltered were not affected by the case.