As the Monday deadline for enrolling in Connecticut’s new health care exchange approaches, many health care experts have judged the exchange to be one of the best run in the country.

Over 190,000 people in Connecticut have enrolled in private insurance or Medicaid as of Sunday, far higher than the 100,000 sign-up target first set by Access Health CT, which manages the exchange. Enrollment, which began after the passage of the federal Affordable Care Act, has recently reached 3,000 to 4,000 people a day, according to Kevin Counihan, the CEO of Access Health CT.

U.S. Sen. Chris Murphy, who said Connecticut’s exchange has been defined by its “lack of glitches,” has voiced strong support for the Affordable Care Act, known colloquially as Obamacare, since its passage.

“Enrollment in the new health care law has totally exceeded our initial expectations,” Murphy said. “In a lot of ways Connecticut has been the model for the entire nation.”

As of Sunday, there are 73,000 people enrolled in insurance plans under the state’s commercial exchange, and the other 117,000 have signed up for the state’s Medicaid program, according to Counihan.

Murphy said the exchange has encountered few setbacks because the governor and the legislative delegation were united in their support of the Affordable Care Act.

“In Connecticut we made a commitment from the top down to implement the law rather than undermine it,” Murphy said. “We had a unity of purpose and a governor who made a really good choice when it came to who he put in charge of the exchange.”

Murphy also pointed to a recent New York Times article that described Connecticut’s website as “smoothly functioning” and said officials are “offering to sell their expertise to states like Maryland,” a state that had severe website problems.

After Monday, the penalty for not enrolling in health care will kick in, which will fine people who have not signed up at 1 percent of their household income or $95, whichever is higher. In the last two days, around 6,000 people have signed up, with around 60 percent going on Medicaid and 40 percent joining the commercial exchange, Counihan said.

“Classic human behavior,” Counihan said, adding that he expects sign-ups on Monday to be “crazy.”

Counihan said the high enrollment numbers are reflective of a functioning website, which is separate from the problem-riddled federal site, as well as standardization across the insurance plans and successful door-to-door outreach efforts to promote the exchange.

He said Access Health CT has been promoting enrollment through social media as well as organizing a team of community outreach workers, church leaders, health center employees, students and health care “navigators” and “assisters” to help people enroll.

The state’s 14 health centers that have been helping people sign up when they come in to receive care have seen steady enrollment in the health care exchange, according to Deb Polun, spokeswoman for the Community Health Center Association of Connecticut.

Polun said staff members at health care centers have been effective in signing people up for insurance because they are already trained, are typically community members who know patients well and can explain insurance in various languages and in ways people understand.

Twenty-nine percent of health care patients in the state are best served in a language other than English, and 75 percent are racial or ethnic minorities, Polun said.

Health Care centers are involved in Access Health’s “March to Enrollment,” with more Access Health CT staff going to centers to boost enrollment right before the deadline.

Access Health CT also set up two “retail stores” to sell insurance, including one at 55 Church St. in New Haven. The New Haven location sees an average of 175 customers per day, Counihan said.

Although enrollment numbers have been higher than expected, the enrollment process has not been without issues.

Polun said that although sign-ups have generally been going well, health centers have experienced some problems with the Access Health website. She said the website sometimes rejects people, says a person is wrongly Medicaid eligible or ineligible or is simply down.

The weekend before the deadline was particularly slow, she added.

Counihan said the slow connections can be attributed to the “unprecedented level of complexity” in the website and the fact that the state’s website connects with federal data, which often loads slowly.

The Gallup-Healthways Well-Being Index showed earlier this month that the uninsured rate, now at 15.9 percent nationwide, has decreased by over a percentage point since the end of last year. Connecticut currently has an uninsured rate of 8 percent, according to Counihan.

The biggest problem facing the exchange right now, Polun said, is communication between Access Health CT and the state’s Department of Social Services, which administers the newly expanded Medicaid program.

The Department of Social Services is in the process of replacing its eligibility system, Counihan said. For now, the department cannot process PDF documents and must retype them into their system.

“It leads to a lot of errors and delays,” Polun said, adding that she has seen the department take months to process Medicaid applications.

Polun said 23 percent of health care center patients are uninsured, and many sign up for Medicaid.

Medicaid enrollment has expanded greatly throughout the country, Murphy said, adding that Connecticut already had a “generous” Medicaid program, so the state did not see as large of a surge in sign-ups as other states experienced.

Counihan said it will take four to five years to see how the legislation ultimately plays out.

“Implementing a massive social program like the Affordable Care Act requires patience, and we live in a highly impatient society,” Counihan said. “There’s going to be people after [Monday] who are going to declare the law a success or a failure, but it’s way too early. It’s going to take a while to adjust.”

The enrollment period for 2015 will run from Nov. 15, 2014 to Feb. 15, 2015.