WASHINGTON — In the orbit of Washington think tanks, the Competitive Enterprise Institute is an obscure name with a modest budget that belies its political connections to conservative titans like the Koch brothers.

But the institute, a libertarian research group, enjoyed a coming-out of sorts on Wednesday, as the lawsuit that it organized and bankrolled — challenging the Affordable Care Act — was heard by the Supreme Court. The case has the potential to end federal insurance subsidies for some 7.5 million people in 34 states.

Until now, the 31-year-old think tank was probably best known as a strident critic of what it calls “global warming alarmism.” It has also been a ceaseless advocate for small government and free markets and has played what the conservative entrepreneur Steve Forbes called “a critical role in preventing the worst of the left’s utopian nightmares from becoming reality.”

But beyond its research reports and policy papers, the Competitive Enterprise Institute has a litigious side, and it has teamed up with state attorneys general to challenge an array of Obama administration regulations on financial, air-quality and other issues.