"In 2015, the smart move is to do window-shopping again. I'd say [for] everybody," Levitt said a day after federal officials revealed details of the automatic re-enrollment for more than 5 million Obamacare customers.
Levitt noted there will be a large number of price changes that could make an expensive plan from 2014 a more attractive option in 2015—and vice versa—when open enrollment on HealthCare.gov begins Nov. 15.
The autopilot option for enrollment could also, in some cases, result in people who had paid no money at all out of pocket for their insurance premiums in 2014—because of the value of the subsidies they get—abruptly learning in January that they now have to personally pay some money each month.
Read MoreObamacare's 95% fix: Auto re-enroll
In other cases, subsidy-eligible Obamacare customers could see double- or even triple-digit percentage hikes in what they pay out of pocket for premiums if they don't switch the insurance plan they have now, he said.
"I think it will be surprising and confusing to many people who face these increases," Levitt said.
Such dramatic percentage hikes for subsidized customers stem from the complicated method the government uses to calculate tax credits for low- to middle-income people to help them pay for insurance sold on Obamacare exchanges.
The method ties the amount of subsidies that a person gets to the price of the "silver" plan sold on the exchanges—even if someone doesn't opt to buy that plan. Silver plans, which cover about 70 percent of health benefits, are as a rule the second least expensive types of plan sold on the exchanges