Democrats said a skeptical public would come around on the new health care law once it started to take effect. But two years and millions of dollars later, the groups that set out to convince Americans to like President Barack Obama’s signature domestic achievement have failed to move the needle.

While the government began defending the constitutionality of the Affordable Care Act’s individual mandate to the Supreme Court on Monday, a battle over the size and scope of government played out on the street outside.

Monday marked the beginning of a three-day sprint for a carefully coordinated campaign organized by liberal groups including Health Care for America Now, Families USA, and Know Your Care and Protect Your Care, political nonprofits launched last year by Massachusetts Gov. Deval Patrick (D).

In the past two years, the groups have spent nearly $25 million promoting the law — and President Barack Obama’s re-election, by default. That spending does not include the investments made by the Center for American Progress and labor unions such as the American Federation of State, County and Municipal Employees and the Service Employees International Union, which helped organize this week’s activities.

Still, support for the law outside Washington is so-so at best, according to recent polls. Polls released by the Kaiser Family Foundation and by the Pew Research Center earlier this month both found virtually no change in public opinion of the law since April 2010. The Kaiser survey found that 23 percent of respondents had a “very unfavorable” opinion of the law, up from 18 percent in 2010.

Supporters of the law dominated the Supreme Court steps Monday, while tea party dissenters saved their energy for a rally targeting Congress scheduled for today. Advocates argued as they have all along that most Americans have yet to benefit from the law because it will not be fully implemented until 2014, and they say the people who already have seen benefits don’t realize the health care overhaul is the cause.

Yet many of the most-buzzed-about provisions have taken effect. Since September 2010, children have been able to stay on their parents’ health care plan until age 26. Last year, senior citizens started receiving free preventive care, and those who reached the gap in Medicare Part D coverage started receiving a 50 percent discount on their prescription drugs.

Nearly 4 million senior citizens have been helped by the change, but that represents just 10 percent of the elderly population, noted David Certner, the legislative policy director at AARP. Senior citizens are waiting to see if the other benefits they count on will change once the law is fully implemented, he said.

Advocacy groups argue that a similar wait-and-see approach is playing out among other populations. Republicans have been very effective at turning opposition to the individual mandate provision into a broad attack on the validity of the entire law. Proponents of the law continue to say the components of the new law are popular, even if the overall legislation isn’t.

Ethan Rome, the executive director of Health Care for America Now, said the constant challenges to the law both in the House and in the court system have worked against them.

“That creates doubt about whether the law is going to be in existence,” Rome said. “I believe strongly that people are going to embrace the law in substantially higher numbers once they believe the law is here to stay.”

Rome’s group spent $53 million campaigning for the law and has spent about $10 million defending it.

But the grass-roots activists who were most fiercely engaged in the legislative battle, especially those who lobbied for the public option, have shifted to other issues. That has left defending the health care overhaul to professional advocacy organizations, and the highly partisan nature of the debate has made things difficult.

“Our coalition is nonpartisan, so we are trying to be careful not to identify ourselves with the Democrats or the Republicans,” said John Rother, the president and CEO of the National Coalition on Health Care, which has spent about $1 million educating health care providers about the new law. “It’s pretty near impossible.”

Indeed, if there is one thing both sides agree on, it is that the controversy over the health care law is really not about the individual mandate, or even health care.

“Those are specifics … that really [don’t] matter to me,” said Gregg Cummings, a member of a Tea Party Patriots chapter in Iowa, who stood outside the Supreme Court on Monday holding the “don’t tread on me” Gadsden flag that has come to signify the movement. “What matters to me is that taxpayer monies are being used to pay for other people’s health care insurance, and that puts our country in greater debt.”