James Wadleigh Jr., the CEO of Connecticut's Obamacare exchange, told CNBC that "open enrollment is going very well" this season.
"We have enrolled 15,000 brand new customers into our system that we haven't seen before," Wadleigh said.
Last year, the Access Health CT exchange signed up about 110,000 customers, and this season "we are hoping to get into the 115,000 range," he said.
Wadleigh noted that the Access Health CT has helped lower Connecticut's uninsured rate from 8 percent in 2012 to 3.8 percent.
But, "I think it's going to be hard for us to keep nibbling away at that number," Wadleigh said.
The remaining uninsured population is considered harder to sign up because they often don't believe they can afford health insurance, and as a group have low familiarity with insurance and the deadlines for enrollment, surveys have shown.