BOSTON — President Barack Obama chose the site where Massachusetts’ health care system became law to promote his signature health insurance program, arguing that the state plan also faced initial setbacks and low enrollment but in time gained popularity and became a success.

“All the parade of horribles, the worst predictions about health care reform in Massachusetts never came true,” he said. “They’re the same arguments that you’re hearing now.”

The Massachusetts’ law provided the model for the federal health insurance overhaul. Obama spoke in Boston’s historic Faneuil Hall, where Massachusetts Republican Gov. Mitt Romney was joined by the late Democratic Sen. Ted Kennedy to sign the state’s 2006 health care overhaul bill.

The president pointed to benefits already available under the 3-year-old health care law, including ending discrimination against children with pre-existing conditions and permission to keep young people on their parents’ insurance plans until they turn 26.

But he conceded the troubled launch of the open enrollment period that began Oct. 1.

“I am not happy about it,” he said.

Underscoring the president’s challenge, the HealthCare.gov website was down, because of technical difficulties, during his remarks. Republicans say the current computer dysfunction is more reason to repeal the law, and they’re pressing Obama administration officials for an explanation.

Obama also tried to clarify the most recent controversy surrounding the law — the wave of cancellation notices hitting small businesses and individuals who buy their own insurance. Obama repeatedly had vowed that people who liked their insurance would be able to keep it.

The cancellation notices apply to people whose plans changed after the law was implemented or don’t meet new coverage requirements. The president said those changes ensure that all Americans are able to get quality coverage.

He said that because of government subsidies, most people who must get new policies will pay less than they do now. But he acknowledged that “a fraction of Americans with higher incomes” will likely pay more.

Romney took issue with Obama’s characterization of the Massachusetts health care law. In a statement, he said “had President Obama actually learned the lessons of Massachusetts health care, millions of Americans would not lose the insurance they were promised they could keep, millions more would not see their premiums skyrocket and the installation of the program would not have been a frustrating embarrassment.” During the 2012 presidential campaign, Romney had pledged to work for the repeal of Obama’s health care law if elected.

Obama, who lived in Boston while a student at Harvard University, was in town for a World Series game day, but his spokesman said he didn’t plan to make a side trip to Fenway Park, mindful of the impact his security entourage has on the public.

While in Boston, Obama also spoke at a fundraiser for House Democrats, where about 60 people dined on Spanish-influenced fare, followed by Red Sox cookies honoring the World Series game being played in town the same night.

Invoking the school shooting in nearby Connecticut and the Boston Marathon bombing, Obama said it had been a “challenging year.” He said he had hoped the tragedies would presage a new spirit of cooperation in Congress, but Americans got obstruction, instead.

“However low people’s estimations were of Washington before the shutdown,” Obama said, “they’re lower now.”