* South Carolina conservative left Senate looking for more influence
* Heritage Foundation immigration study tests clout of new leader
By Caren Bohan
WASHINGTON, May 6 (Reuters) - When Jim DeMint announced in December that he was leaving the U.S. Senate to head the Heritage Foundation think tank, he said he thought he could wield more influence outside rather than inside the Congress.
Any doubt about that may have been put to rest on Monday with the release of a study by the foundation lambasting a bipartisan immigration proposal in the Senate as a budget-buster that would cost taxpayers trillions of dollars.
While the report was written by a scholar, Robert Rector, the main attraction was DeMint. That was true for boosters of the study and, as it turned out, for as detractors as well, who used DeMint's name to discredit the findings.
The publicity tour started on Sunday when the former South Carolina senator plugged the Heritage study on ABC's "This Week," not normally a venue for think-tank wonks.
It continued on Monday with DeMint defending it in advance on Fox News. Hours later, DeMint presided at the news conference where the report was released.
"He obviously has some influence as a former senator," said Tevi Troy, a former deputy secretary of the Department of Health and Human Services under President George W. Bush.
Troy said the immigration fight would be an "interesting test case" of Heritage's clout since it is the first big issue it is taking on under DeMint's leadership.
Having DeMint as the star cut both ways, however. He is a long-time opponent of immigration reform and as a senator he helped kill a similar bill in 2007. Critics of the Heritage Foundation report - and there were many - used that fact to attack the study.
Among the most outspoken was Haley Barbour, the ex-governor of Mississippi and former head of the Republican National Committee. He noted pointedly on a conference call with reporters that "it was probably more than a coincidence" that Heritage, under DeMint, would be opposing the immigration bill. The study, Barbour said, "is a political document."
DeMint's "reputation as a researcher is, um, questionable," said a statement from America's Voice, a liberal advocacy group that favors the Senate legislation.
The content of the Heritage study was controversial enough. It estimated that the bill's provisions giving undocumented immigrants a 13-year path to citizenship - "amnesty" in DeMint's words - would cost $6.3 trillion over a lifetime because of government benefits that would be paid to them.
Conservative critics of the study called it deeply flawed because it failed to consider the benefits to the economy of the bipartisan immigration bill, which includes provisions sought by industry to fill high-tech and low-tech jobs that companies say are going begging.
The foundation said it followed respected scholarly methodology in producing the study. "We are a research institution here," said Derrick Morgan, a Heritage vice president. "We can't necessarily speak to the motivations of other people. "But we very much want the fiscal costs to be part of the debate because it protects the American taxpayer."
The argument about the study, which took place just days before debate is scheduled to begin on amendments to the Senate immigration bill, marked the opening salvo in a war of talking points and studies that will play out over the next few months.
Heritage is at odds with liberal think tanks such as the Center for American Progress and also with analysts at the libertarian Cato Institute as well as some scholars at the conservative American Enterprise Institute.
The divisions mirror a split within the Republican party itself, with stalwarts such as Barbour as well as Florida Senator Marco Rubio, a rising star within the party, supporting immigration reform. Others such as Senator Jeff Sessions of Alabama and Senator Ted Cruz of Texas have lined up against it.
DeMint, a leader in the conservative Tea Party movement, is known for his outspokenness. In 2009, he helped to fire up conservative opposition to President Barack Obama's proposal to overhaul the healthcare system by declaring that the bill would Obama's Waterloo. Republicans were unable to stop the bill from becoming law.
DeMint's role is all the more interesting because of his ties to Rubio, a member of the so-called Gang of Eight senators who wrote the immigration reform bill under consideration.
DeMint was a strong supporter of Rubio's Senate candidacy in 2010 and the Florida senator, who is seen as a possible presidential candidate in 2016, has credited DeMint with helping him to win the seat.
"Immigration reform pits Rubio against mentor DeMint," said a headline on a CNN blog post.
"By the time that appeared on Monday afternoon, DeMint, unfazed, was back on television, telling Fox News: "what we need to do is put aside this whole idea of amnesty and fix our system one piece at a time."
The immigration bill, he said, "is going to be another Obamacare." (Additional reporting by Thomas Ferraro. Editing by Fred Barbash and Christopher Wilson)