Obamacare requires most employers to offer coverage next year, but fears persist that many will dump workers onto the insurance exchanges instead. Fear not, for now.

Q: I’ve heard that some firms may drop their health plans and have workers purchase a plan on the government exchanges. Will that happen to me?

A: Nine months after the launch of the controversial health insurance exchanges, confusion hasn’t died down over what exactly health reform means for the average American. A new poll found that 65% of workers are very or somewhat worried that their firms will drop health coverage and have employees go it alone on the new federal and state insurance exchanges.

Such a move would hurt, at least in workers’ minds, according to the survey of 1,240 likely voters by Morning Consult, a digital media company. Half said that if their employer exited the benefits business, they would be negatively affected; only 16% expected to benefit from such a switch.

Even though Obamacare requires firms with 50 or more workers to offer insurance or owe a fine starting in 2015, the concern is that some will opt to pay the fine, since individual coverage can cost two to three times as much—and substantially more for a family plan. What’s more, employers with fewer than 50 workers that already offer health benefits—even though they are not required to—may decide to get out of the business now that all workers have the alternative of buying coverage on an exchange.

Are workers right to worry about getting dumped? As long as you work for a large firm, you shouldn’t lose sleep over the issue, at least not yet, says Beth Umland, director of research for health and benefits at consultant Mercer. Earlier this year—well after the exchanges went live—an overwhelming 94% of big firms reported that they will keep offering health coverage for the next five years, Umland says. That percentage has remained consistent since Mercer first asked the question in 2008.

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Jeffrey R. Ungvary President