Obama administration officials argue the bulk of Americans who eventually enroll in insurance coverage under the new health care law will do so in late November and early December and then early next year, giving the government at least several more weeks to iron problems that have plagued the launch of the new insurance options under the Affordable Care Act, particularly the website HealthCare.gov.

At a briefing with reporters on Monday afternoon, senior officials acknowledged the struggles many Americans have had with the website and repeated the view of President Obama that the problems are “unacceptable.” But citing data from Massachusetts, which implemented a similar kind of comprehensive health insurance plan in 2007 and 2008, administration officials say that the bulk of enrollment in the health care law is likely to happen ahead of two deadlines.

The first is Dec. 15, the date by which people must purchase insurance that would begin on Jan. 1. The second is around March 31, when “open enrollment” for health insurance for 2014 ends, and Americans who do not get insurance by then would face a fine of either $95 or 1 percent of their income, whichever number is higher.

In Massachusetts, enrollment surged in December 2007, a month before the requirement to buy insurance or pay a fine kicked in. (This article from the New England Journal of Medicine illustrates that trend, as first reported by the New Republic‘s Jonathan Cohn.) Obama officials said that they expect a similar”spike” in enrollment in December 2013 and then another one in February and March.

Late November and early December is “when the real shopping begins,” said a senior White House adviser involved in implementing the health care law. (The briefing was conducted on the ground rules that reporters could not quote the officials by name.)

White House officials said there are a few signs the law is already working. They highlighted the more than 50,000 people in Oregon who have signed up for Medicaid over the last few weeks because of the increased funds for that program through the health care law, as well as the successful health care websites in states like Kentucky and Connecticut.

“The product is good, the price is right,” said one senior official, adding,  “we feel good about the law.”