President Obama took some serious heat last year when insurers started dropping millions of Americans from health plans that were no longer Obamacare-compliant, seemingly breaking his promise, "If you have insurance that you like, then you will be able to keep that insurance."

A new study, however, backs up the administration's claims that the cancellations were part of the normal churn of the individual health market.

After analyzing patterns in the nongroup health coverage market from 2008 to 2011, Harvard professor Benjamin Sommers found that the market was characterized by high turnover before the Affordable Care Act was implemented. Additionally, Summers found that most people who left the nongroup market acquired other insurance within, suggesting that the cancellations attributed to Obamacare are unlikely to have a significant impact on overall coverage rates.

Relying on data from the Census Bureau's Survey of Income and Program Participation for his study, Sommers used a sample of 4,199 respondents under 65 years old with nongroup coverage in their first month in the survey.

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Over one-third of those respondents no longer had nongroup insurance coverage after just four months, Sommers found. Just 42 percent had stable nongroup coverage after one year. After two years, just 27 percent had stable coverage.

Given that there were an estimated 10.8 million people in the nongroup market in 2012, as many as 6.2 million people could be leaving that market place in a given year, Sommers notes. "This suggests that the nongroup market was characterized by frequent disruptions in coverage before the ACA and that the effects of the recent cancellations are not necessarily out of the norm," he wrote in the study's abstract.

Additionally, Sommers found that most people leaving the market found coverage elsewhere: Fifty percent of people who experienced a coverage change found employer-sponsored insurance by the study's first year. Another 20 percent had regained nongroup coverage, 6 percent had Medicare or Medicaid, and 4 percent had other coverage. The remaining 20 percent were uninsured a year into the study.

Given that two-thirds of the sample had incomes at or below 400 percent of the poverty line, the study suggests that most people in the nongroup market would be eligible for federal subsidies on the new Obamacare marketplaces or Medicaid coverage.

Sommers' study is the first to take a nationwide look at stability in the pre-Obamacare, nongroup health insurance market. Other research focused on the nongroup market at the state level, but there has been significant variation across different regions.

When news started trickling out about consumers losing coverage -- presumably because their bare-bones insurance plans on the individual market did not meet Obamacare's minimum coverage standards -- Mr. Obama defended his law, pointing out that insurers "routinely dropped thousands of Americans every single year."

Yet after continued public outcry, Mr. Obama enacted an administrative policy change allowing insurers to extend existing plans on the individual and small-group markets. By the time this transitional policy fix ends in 2017, the administration expects most people on the nongroup market will have found stable coverage on the Obamacare marketplace or elsewhere.

"By the time it gets to 2016, I don't think under any circumstances there's going to be a wave of cancellation notices," an administration official told reporters in March.