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* Republican leaders' shift on immigration after election
* Some fear party risks irrelevancy by alienating Hispanics
* Bipartisan plan's biggest hurdle likely to come in House
By John Whitesides
WASHINGTON, Jan 29 (Reuters) - What a difference one brutally disappointing election can make.
At this time last year, Republican U.S. presidential contenders were competing to act tough on immigration to win favor with the party's conservative base.
Eventual nominee Mitt Romney led the way by advocating "self-deportation" - a plan that essentially called on the government to make life so miserable for the nation's 11 million illegal immigrants, most of whom are Hispanics, that many would leave on their own.
But since Democratic President Barack Obama's decisive victory over Romney in November with the support of more than seven in 10 Hispanic voters, the game has changed.
Many Republicans now see gaining favor with the fast-growing Hispanic voting bloc, which accounts for 10 percent of the U.S. electorate and is growing, as a matter of political survival.
Some remain critical of any plan that would give illegal immigrants a path to citizenship. But next-generation Republican leaders - including Florida Senator Marco Rubio, 41, a favorite of the conservative Tea Party movement - are desperate to remove the issue as a liability for the party.
That is why a plan announced on Monday by a bipartisan group of eight U.S. senators including Rubio is widely seen as the best hope in years for a comprehensive immigration overhaul - even though it is similar to a 2007 plan that was shot down by conservative Republicans despite being backed by Republican President George W. Bush.
But now, "the politics on this issues have turned upside down," said New York Democrat Chuck Schumer, another senator in the bipartisan group crafting the immigration plan.
"For the first time ever, there is more political risk in opposing immigration reform than in supporting it," Schumer said.
REPUBLICANS LOSING HISPANIC SUPPORT
Compared with the bitter, uncompromising politics that have clouded Capitol Hill in recent years, the news conference held by the senators on Monday was practically a festival of love.
There was Republican Senator John McCain of Arizona - who lost the presidential race to Obama in 2008 and is a frequent critic of the administration - heaping praise on the Democratic president for supporting immigration reform.
There was Democratic Senator Dick Durbin of Illinois, giving credit to Bush for backing immigration changes when many Republicans did not.
During the news conference, Rubio and Democrat Robert Menendez of New Jersey, another member of the group, made a point of explaining parts of their plan in Spanish, a symbolic reach-out to those who could be affected by it.
The changed dynamic on immigration reflected how "the election was a real wake-up call to Republicans. They have had their eyes opened on Hispanics," said Steven Schier, a political scientist at Carleton College in Minnesota.
Asked why he thought this immigration bill might succeed, McCain said: "Elections. The Republican Party is losing the support of our Hispanic citizens."
Republican strategist Ana Navarro said McCain - whose state borders Mexico and is about 30 percent Hispanic - could be an important voice to other Republicans on the immigration bill.
"Nobody can talk to other Republicans with the authority that John McCain can about what it means to move the Latino vote," Navarro said.
'AN IMPORTANT FIRST STEP'
The group of senators behind the immigration plan - which also includes Republicans Jeff Flake of Arizona and Lindsey Graham of South Carolina and Democrat Michael Bennet of Colorado - said they hoped for quick action.
But even if successful, Congress' revamping of the immigration system is likely to take most of 2013. Congress also will be wrestling with budget issues and Obama's ambitious gun-control proposals in the next few months.
"Today is an important first step in what is going to be a significant and complicated journey," Rubio said.
The plan would create what the senators called a "tough but fair" path to citizenship for many illegal immigrants after undefined improvements to border security and a crackdown on people who have overstayed their visas.
The plan faces some hurdles in the Senate. But the big question will be whether it can clear the Republican-led House of Representatives, which is dominated by conservatives adamantly opposed to anything resembling "amnesty" for illegal immigrants.
One rising star among House conservatives - Paul Ryan, the Budget Committee chairman who was Romney's vice presidential nominee - already has voiced support for Rubio's immigration efforts. Others seem to be loading up to attack such a plan.
"When you legalize those who are in the country illegally, it costs taxpayers millions of dollars, costs American workers thousands of jobs and encourages more illegal immigration," Representative Lamar Smith, a Texas Republican, said in a statement.
Many conservatives said they would wait for the final proposal, which will be developed by the Senate Judiciary Committee. Senate Republican leader Mitch McConnell said the final measure will require far more input than it has received so far.
"All members must have an opportunity to debate and amend any legislation that comes to the floor. This effort is too important to be written in a back room and sent to the floor with a take-it-or-leave-it approach," McConnell said. "It needs to be done on a bipartisan basis and include ideas from both sides of the aisle."
Groups that oppose easing the immigration restrictions blasted the plan and predicted that it would meet the same fate as the 2007 bill.
"We expect that once the American public learns of the details of this proposal, and comes to recognize that it will do nothing to fix the problems of our broken immigration system, it will meet with the same overwhelmingly negative response that it received in 2007," said Dan Stein, president of the Federation for American Immigration Reform.
But backers of a comprehensive immigration plan said there was a new mood of optimism in their ranks.
"The histrionics and demagoguery on immigration have died down, at least for now," said Fergus Cullen, a former chairman of the New Hampshire Republican Party who has launched an immigration reform group.
"There seems to be a different attitude," Cullen said. (Additional reporting by Steve Holland; Editing by David Lindsey and Will Dunham)