Congressman Peter King speaks to his new constituents at Villa...

Congressman Peter King speaks to his new constituents at Villa Lombardi's in Holbrook. (Oct. 23, 2012) Credit: Johnny Milano

The Republican Party has begun a debate on how it should appeal to Hispanics, the nation's fastest growing group, after a record Latino turnout helped President Barack Obama win re-election Tuesday.

A key issue is whether the Republican Party should soften its hard-line positions on immigration that have alienated Latinos, or whether it should simply find a better way to sell its policies to Hispanics, analysts and lawmakers said Wednesday.

"We have a Latino problem that just cost us a national election," GOP strategist Mike Murphy said on NBC Tuesday night. "We're going to have to have a very adult conversation that might turn into an intraparty fistfight about how we become electable again."

It's a question being weighed by immigration hard-liner Rep. Pete King (R-Seaford). His own district has gone from 2 percent black and Hispanic to 32 percent after it was redrawn and moved to the South Shore this year. He won with 59 percent of the vote this year, but could face a tougher opponent next time.

King said he believes he should stick to his principles. But he acknowledged that for the Republican Party, "It might be easier if we change our policies. Politically, we may end up changing them."

Republicans have long been split on the issue of immigration, and the debate going on now is not easy to resolve.

Some say the party should drop its harsh rhetoric about illegal immigrants and avoid moves such as Arizona's immigration law, which allows police to check papers of people they deemed suspicious.

Others defend those laws as necessary in the onslaught of illegal immigration, particularly in the Southwest from Mexico.

The GOP could be forced to make a decision on its Hispanic strategy as soon as next year.

Senate Democrats could act on Obama's call to take up a comprehensive overhaul of immigration law, putting Republicans on the spot for the 2014 midterm elections.

The debate began after exit polls Tuesday found Hispanics for the first time cracked 10 percent of the electorate, and that 71 percent of the Latino vote went to Obama, up from 56 percent for the Democratic candidate in 2004.

Some Republican strategists, including Karl Rove and Michael Dawidziak of Bohemia, advocate that the party adopt more Latino-friendly policies.

As President George W. Bush's adviser, Rove pushed a comprehensive immigration overhaul that included a path to citizenship for noncitizens here illegally — a measure blocked by the House GOP.

"If you want Hispanics," said Dawidziak, "you're not going to get them unless you have a sane policy on immigration."

Others, such as Florida GOP Sen. Marco Rubio, said it's a matter of getting a message across. Conservatives have an appeal to immigrants trying to make it, he said, "and Republicans need to work harder than ever to communicate our beliefs to them."

Not everyone is convinced the Latino vote was decisive.

"Obama won because the economy was growing just fast enough to push him over the finish line," said John Pitney, a scholar at Claremont McKenna College in Claremont, Calif.

"In the longer run, the Hispanic vote is going to be an increasing problem for the Republican Party," Pitney said.

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