About 3.4 million previously uninsured Californians — 58 percent — report getting health insurance since last summer, according to new data from the Kaiser Family Foundation, but the remaining uninsured may be nearly impossible to reach.

"Expanding coverage gets harder from here," Kaiser Family Foundation CEO and President Drew Altman said. "Most of those who remain uninsured have gone years without coverage, and many are immigrants who don't qualify or are worried about drawing attention to family members' immigration status."

"Among the 42 percent who remain uninsured, many have characteristics that traditionally make them hard to reach with health coverage," the report read. "Among this group, 37 percent say they have never had health insurance, and another 45 percent say they have been uninsured for two or more years. Most have low-to-moderate incomes."