WASHINGTON, April 4 (Reuters) - When President Barack Obama renewed his political battle with the U.S. Supreme Court this week, he was drawing on the experience of another Democratic president, Franklin Roosevelt, who fought the court some 75 years ago.

Obama criticized the possibility the court will strike down his healthcare law when it rules on the case, angering Republicans and even drawing counter-fire from a U.S. appeals court judge in another case.

In 1936 Roosevelt, angry at the rejection of some of his "New Deal" social and economic programs following the Great Depression, proposed legislation that would have allowed him to appoint a new justice for every sitting justice over 70.

The proposal, which became known as Roosevelt's "court packing" legislation, died in the face of widespread opposition, including from fellow Democrats, and after a shift by the Supreme Court in upholding his programs.

It is rare but not unheard-of for a president to comment on a pending Supreme Court case. More unusual was the response to Obama's remarks from federal Judge Jerry Smith, a Republican appointee, in a case stemming from the healthcare law.

At a court hearing in New Orleans on Tuesday, Judge Smith demanded a letter by Thursday from Attorney General Eric Holder on whether the Justice Department recognizes that judges have the power to strike down unconstitutional laws.

LATEST ROW

Obama ignited the latest row on Monday when in blunt language he said striking down the healthcare law would amount to an "unprecedented, extraordinary step" of "judicial activism," the very charge that conservative Republicans have leveled against the court for years.

In remarks on Tuesday that seemed more conciliatory, Obama referred back to the history from the 1930s, saying that had been the last time the Supreme Court overturned a law passed by Congress intended to address an economic problem such as healthcare regulation.

"The point I was making is that the Supreme Court is the final say on our Constitution and our laws, and all of us have to respect it, but it's precisely because of that extraordinary power that the court has traditionally exercised significant restraint and deference to our duly elected legislature, our Congress," he said.

In his remarks Obama appeared to signal how, if the court strikes down the law passed two years ago, he might turn the court's 5-4 conservative majority into a campaign issue ahead of the Nov. 6 election, in which he seeks a second four-year term.

The court will decide for the first time whether Congress overstepped its powers by requiring most Americans to buy health insurance by 2014, whether they want it or not.

Jeff Shesol, author of the book "Supreme Power: Franklin Roosevelt vs. The Supreme Court," said there were historical and legal parallels between the battle now and the one in the 1930s.

"The question at the core of the New Deal case is the question at the core of the present case -- the ability to create national solutions to national problems," said Shesol, a White House speechwriter when Bill Clinton was president.

Northwestern University Law School professor Eugene Kontorovich said Obama could be expected to argue against the high court overturning the law since that was what his own advocates at the court argued last week.

"There's no constitutional problem, there's no obvious impropriety, and one might even say that the plaintiffs are talking about their case all the time ... so maybe why shouldn't he talk about the case?" he asked.

Kontorovich did take issue with the notion raised by Obama's comments that overturning a law passed by a strong majority in Congress would be unprecedented, saying that laws were ruled unconstitutional periodically.

NO SWAY

Earlier in his career, Obama taught constitutional law at the University of Chicago, but his comments on the judiciary will have no sway with the justices themselves, said Tom Goldstein, a lawyer who argues before the court and is a founder of SCOTUSblog, a website that follows the court.

"The court is going to do what it does and what it thinks is right," Goldstein said.

Obama was on solid legal ground with his comments, Goldstein added. "He certainly wasn't challenging judicial review, and he's right that it has been many decades since the Supreme Court struck down a statute as significant as this one."

The Supreme Court's healthcare ruling is expected by the end of June, in the midst of the presidential campaign. All of Obama's would-be Republican challengers oppose the law and have vowed to repeal it.

At a Medicare fraud summit in Chicago on Wednesday, U.S. Attorney General Eric Holder said the administration would respect the court's decision.

The critical remarks were not the first Obama had directed at the Supreme Court.

In his 2010 State of the Union address, Obama criticized the court ruling known as Citizens United, which gave corporations the constitutional free-speech right to spend unlimited amounts of money to support or oppose candidates for federal office.

Justice Samuel Alito, one of six justices sitting directly in front of the president at the time, shook his head and mouthed the words "not true" when Obama said that ruling "reversed a century of law" and would open the floodgates for special interests to influence elections.

Chief Justice John Roberts, who may control the outcome in the healthcare case along with moderate conservative Justice Anthony Kennedy, later said he found the State of the Union incident "very troubling" and compared the atmosphere to a "political pep rally."

Rulings on such controversial issues as abortion have made the court a political issue at election time for some years, drawing criticism from both parties. During the 2000 campaign, George W. Bush came out against judicial activism. He said he believed judges should not take the place of legislators.

In 1968, when Republican Richard Nixon ran for president, he campaigned against the Supreme Court and complained that the liberals under Chief Justice Earl Warren had given too many rights and legal protections to criminal defendants.

(Reporting by James Vicini; Additional reporting by Jeremy Pelofsky and Joan Biskupic in Washington and Jessica Wohl in Chicago)

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