This year, many enrollees have added questions as the Trump administration and legislators in Washington dismantle the Affordable Care Act, often referred to as Obamacare, which established the marketplace and created penalties for people who forgo health insurance. Yes. “Though consumers may have concerns about the future of the Affordable Care Act, as of now, nothing has changed about the fourth enrollment period - not plans, not prices, and not dates,” according to Enroll America, which seeks to get the uninsured signed up for coverage.