RICHMOND — Ken Cuccinelli II, the first state attorney general in the nation to sue over the federal health care law, has hit upon a new anti-‘‘Obamacare’’ strategy that is much easier than going to court: Do nothing.

Virginia and other states can shield businesses from hefty fines for not providing adequate health insurance for employees, he contends, simply by refusing to set up their own state-based insurance exchanges.

Cuccinelli bases that legal theory on a quirk in the law, one variously attributed to sloppy drafting, political miscalculation, or both: It includes a provision to impose those fines under state-based exchanges, but not under a federal one.

Supporters of the law acknowledge the wording glitch but say the matter has been clarified through regulations subsequently issued by the Internal Revenue Service. They dismiss Cuccinelli’s line of attack as wishful thinking or willful distortion.

Crafted by a Cato Institute scholar about a year ago, the theory started quietly making the rounds among conservative think-tank scholars, attorneys general, lawyers, and bloggers while the matter was before the Supreme Court. It has picked up steam since the court upheld the law in June.

For Affordable Care Act foes who first tried to kill the law in the courts and now aim to do so by electing Republican Mitt Romney president, the do-nothing approach is a long-range Plan C.

‘‘This could bring down the entire law,’’ said Michael F. Cannon, the Cato Institute’s director of health policy studies who crafted the argument.