* Boehner, McConnell praise bipartisan efforts
* Tea Party's Rand Paul embraces comprehensive reform
* Group of Senate Republicans wants to put brakes on bill (New throughout)
Leading Republican U.S. lawmakers, moving to repair frayed relationships with Hispanic voters, on Tuesday put their weight behind comprehensive immigration reform efforts that will likely include a pathway to citizenship for undocumented foreigners.
Speaker John Boehner praised a bipartisan plan emerging in the House of Representatives that includes an arduous pathway to citizenship for 11 million people living in the United States illegally.
While he did not specifically endorse allowing the 11 million to become American citizens, Boehner told reporters that the House effort "is frankly a pretty responsible solution."
Boehner spokesman Michael Steel said that the Speaker "has not embraced any one solution, but believes it is important for our members to continue to work and make progress on this issue."
Immigration advocacy groups are hoping to see a reform bill enacted this year, before the 2014 campaigns for Congress heat up, potentially polarizing Democrats and Republicans.
With a wave of support building on immigration reform, "it is becoming increasingly difficult for the naysayers in the Republican Party to gain any traction" in the immigration debate, said Angela Kelley, an immigration specialist with the liberal Center for American Progress
Meanwhile, Senate Republican leader Mitch McConnell had kind words for a bipartisan bill that is expected to be unveiled in coming weeks, which also will contain a pathway to citizenship.
"I think we're all encouraged by the work of the group of eight senators," said the Kentucky Republican.
In addition, one of the most conservative members of the Senate - a Tea Party activist Rand Paul of Kentucky - delivered a speech to a Hispanic business group Tuesday in which he ridiculed the notion of deporting the 11 million people, many of whom have lived for decades in the United States and are raising families here.
Instead, in a speech peppered with Spanish that he read off a Teleprompter, Paul said he would offer legislation that would set up a "probation period" for those living here illegally.
A major immigration reform bill could hit the Senate floor in June or July under a schedule sketched out by a bipartisan group now writing legislation. Paul likely would try to amend that bill with some of his own ideas.
"Somewhere along the line, Republicans have failed to understand and articulate that immigrants are an asset to America, not a liability," said Paul, who has hinted at a possible 2016 run for president.
In November's presidential election, Republican candidate Mitt Romney received an anemic 27 percent of the Hispanic vote, provoking soul searching among party leaders.
While Republicans desperately want to be able to lure support from the fast-growing Hispanic voting bloc, they have been struggling how to frame their law-and-order message that is challenged by the idea of granting citizenship to those who have come to the United States illegally.
Speaking to reporters following his speech, Paul was pressed on whether his probation period would lead to citizenship. He did not specifically say that it would but essentially described a process under which illegal immigrants eventually would become Americans.
Paul said his goal was to "normalize" this large group of people in stages by granting them work visas once annual reviews of U.S. border security were approved by Congress.
After that, Paul said, undocumented immigrants would "get in the line to come in the country which is how you become a citizen ... like anybody else. But you wouldn't go to the front of that line and you wouldn't have to leave the country" while awaiting citizenship, he said.
Nervous that his comments were being misconstrued, Paul's office arranged a telephone press conference later on Tuesday to clarify his position on granting illegal immigrants citizenship. But he did not step back from the stance he outlined earlier in the day.
NOT SO FAST
Even with President Barack Obama putting immigration reform at the top of his 2013 agenda, any bill faces a difficult road this year and a group of Senate Republicans served warning that legislation should not move too fast.
The six senators, most of them veterans and including John Cornyn, the second-ranking Senate Republican, wrote in a letter to Senate Judiciary Committee Chairman Patrick Leahy: "We respectfully request that the public be given adequate time ... to read and analyze the contents of any such bill" before it moves through the panel, possibly next month.
The senators reminded Leahy that there were years of debate before passage of the last major immigration reform in 1986.
One of the senators, Jeff Sessions of Alabama, told reporters that Congress should act to treat the 11 million undocumented "fairly and decently."
But he repeated his strong opposition to citizenship. "You might get legalized, your children might be citizens ... but you don't get every benefit if you come to the country illegally. We must adhere to that principle," Sessions said.
Paul, who arrived in the Senate in 2011, already is winning a reputation as an important player in the 100-member chamber. Earlier this month he staged a filibuster in the Senate - essentially a talk-a-thon - to spotlight the Obama administration's growing use of drones in anti-terrorism efforts.
Asked whether he would try to stand in the way of an immigration reform bill if his ideas were not incorporated, Paul was non-committal.