* Law may be constitutional, but it's not popular
* Romney raises more than $1.5 million after decision
* Repeal will be difficult if Romney is elected (Updates/edits in paragraphs 15 and 18)
By Andy Sullivan
WASHINGTON, June 28 The battle over President Barack Obama's landmark healthcare law shifted from the Supreme Court to the campaign trail on Thursday, as Republican challenger Mitt Romney asked voters to throw Obama out of office to get rid of the unpopular law.
The high court's 5-4 decision to uphold the law was a setback for Romney and his fellow Republicans, who had hoped that Obama's central policy achievement would be struck down as unconstitutional.
But the overhaul remains unpopular, and Romney cast the Nov. 6 presidential election as the best chance for voters to overturn it.
"Our mission is clear: If we're going to get rid of Obamacare, we're going to have to replace President Obama," Romney said on the roof of a building overlooking the U.S. Capitol.
Most Americans oppose the law even though they strongly support much of what it does, according to a Reuters/Ipsos poll released on Sunday. Obama's Democrats acknowledge that they have done a poor job of selling the Affordable Care Act, as it is known, and they suffered steep losses in the 2010 congressional elections that followed the law's passage.
While the court decision avoids an embarrassment for Obama in an election year, it could energize conservative voters who were slow to warm to Romney during a months-long battle for the Republican party nomination.
More than $1.5 million in donations poured in to Romney's campaign in the hours following the decision, according to an aide.
Romney could benefit from $9 million worth of ads attacking the law that Americans for Prosperity, a conservative group, said it would air in 12 battleground states starting on Friday.
The decision could also help Romney win undecided voters, who oppose the law by a four-to-one margin, according to the Reuters/Ipsos poll.
"This is great politically. Bad for the country, but great politically," a Romney adviser said.
Still, it remains to be seen whether the decision will truly shape the contours of a presidential race in which concerns about the shaky economy have crowded out issues like healthcare and the war in Afghanistan.
"For both sides, it's steady as she goes. Obama doesn't have the hurdle of explaining how his program was struck down, but Romney still has the broad doubts within the general public about the program," said Cal Jillson, a political science professor at Southern Methodist University in Dallas.
Romney cast his opposition to the law in economic terms, arguing that its tax increases and new regulations would hurt job creation and the overall size of the program would increase the national debt.
"If we want good jobs and a bright economic future, for ourselves and for our kids, we must replace Obamacare," he said.
He repeated his claim that it would cut the popular Medicare health program for the elderly by $500 billion. Independent groups have disputed that, saying Obama's law would reduce the projected cost of the government-run plan over the coming 10 years without reducing benefits.
The reasoning in the court decision also gives Republicans a new talking point by casting the law's most controversial element - a requirement that individuals must buy health insurance or pay a penalty - as a tax, rather than a mandate.
REPEAL COULD BE TOUGH
Romney's vow to repeal the law could prove difficult. Even if his fellow Republicans win both chambers of Congress in the Nov. 6 elections, Democrats, who control the Senate, will likely retain enough seats in the chamber to keep the law in place.
The Republican-controlled House of Representatives voted to repeal the healthcare law last year and has scheduled another repeal vote for July 11. The measure has little chance of passing the Senate.
Romney also must explain the awkward fact that he signed a similar healthcare law while governor of Massachusetts.
"He owes the American people a clear, non-parsed explanation of why he believes his decisions in Massachusetts are wrong for the country, and exactly what he would do to help the American people get the health care they need," said Obama campaign manager Jim Messina.
Romney has begun to say what changes to healthcare he would make if he were to repeal Obama's law, but he has yet to lay out specifics.
On Thursday, he said he would prohibit health insurers from denying coverage to sick people - a central element of Obama's law - and help states take their own approaches to expanding coverage to the uninsured. He also called for measures to rein in healthcare costs, but did not specify how he would do so. (Additional reporting by Steve Holland, Deborah Charles and Alina Selyukh.; Editing by Alistair Bell and Christopher Wilson)