WASHINGTON (CBSDC/AP) — It was supposedly a big win for President Barack Obama and his administration Thursday when the Supreme Court ruled to uphold the Affordable Care Act, including the individual mandate.

“Whatever the politics, today’s decision was a victory for people all over this country whose lives will be more secure because of this law and the Supreme Court’s decision to uphold it,” Obama said.

People all over the country may not agree with that assessment, however, as confusion and disagreement over the bill that festered well before the ruling had even been written cropped up once again.

It has been a long two-year battle for the White House after Obama signed the health care bill into law as Republicans and several states sought to repeal it. The passage of the law in 2010 also hurt the Democratic Party during the mid-term elections as 64 House seats changed hands to Republicans.

Even during testimony before the Supreme Court earlier this year, several justices questioned the validity of the law, making many wonder if the health care law would be ruled unconstitutional.

But in a 5-4 ruling, with Chief Justice John Roberts being the surprising swing vote and siding with the liberal bloc of the court, they upheld the constitutionality of the health care law.

Democrats are acutely aware the public is still not solidly behind the policy and that the high court’s ruling may have energized Republicans. But cloistered Thursday on Capitol Hill, they savored the moment. Some spoke of the late Massachusetts Sen. Edward M. Kennedy, the Obama patron who pushed for national health care for decades, but did not live to see it signed into law.

Despite the White House and Democrats glowing over the victory, Obama could be the one facing a public backlash of the decision.

A CBS News/New York Times poll released earlier this month showed that 41 percent of the people wanted the health care law overturned, while 27 percent wanted to keep the law, but strike down the individual mandate.

Stu Rothenberg, editor of the nonpartisan Rothenberg Political Report, believes the president will have to walk a fine line with what to say about the health care ruling going forward.

“Clearly, the public is not enamored with the health care law,” Rothenberg told CBS News. “On the one hand, [Mr. Obama] wants to take credit for it and wants to talk about addressing a tough issue — that does show leadership. On the other hand, showing leadership on a matter of public policy on which [voters] don’t approve may not get you any points.”

Another poll from Rasmussen Reports shows that 54 percent of Americans wanted the Supreme Court to rule the law unconstitutional.

“For something as fundamental as medical care, government policy must be consistent with deeply held American values,” Scott Rasmussen wrote on Rasmussen Reports in March. “That’s why an approach that increases consumer choice has solid support and a plan that relies on mandates and trusting the government cannot survive.”

The public backlash against the Supreme Court ruling also helped line the pockets of Mitt Romney’s presidential campaign as it raked in over $4 million Thursday.

Romney said that the only way to repeal Obamacare was by voting Obama out of the White House.

“If we want to get rid of Obamacare, we’re going to have to replace President Obama,” Romney said from a rooftop in Washington overlooking the U.S. Capitol. “What the court did not do on its last day in session, I will do on my first day if elected president.”

House Majority Leader Eric Cantor, R-Va., said the House will vote on repeal of the law July 11. With Democrats in control of the Senate, however, the repeal effort appears doomed for now.

Cantor said the court’s decision “really indicates that we have entered an age in which government — Washington — will be controlling health care unless something changes.”

Despite the ruling, Larry Sabato, director of the Center of Politics at the University of Virginia, told CBSDC that he believes health care will “probably remain a secondary issue” come November.

“What seems like a huge story today probably won’t be as important as the election draws nearer,” Sabato said. “This election is still about the economy, and the state of the economy will be the biggest factor in determining the result.”

(TM and © Copyright 2012 CBS Radio Inc. and its relevant subsidiaries. CBS RADIO and EYE Logo TM and Copyright 2012 CBS Broadcasting Inc. Used under license. All Rights Reserved. This material may not be published, broadcast, rewritten, or redistributed. The Associated Press contributed to this report.)