by Elizabeth O'Brien Open enrollment began on Sunday for the 11.4 million Americans who have individual health insurance through healthcare.gov or their state marketplace, and for new consumers who want to enroll in Obamacare for the first time. A cloud of uncertainty hangs over open enrollment this year. On Nov. 10, the Supreme Court is set to hear oral arguments in a lawsuit that seeks to overturn the Affordable Care Act, also known as Obamacare. A ruling is expected by June, 2021.