(Corrects Cantor's age to 49 in paragraph 15)
* Chief Obama critic says he hopes to work with president
* Cantor calls for initiatives in education, healthcare, immigration
WASHINGTON, Feb 5 (Reuters) - Eric Cantor, the combative second-ranking Republican in the U.S. House of Representatives, launched a major rebranding of his party on Tuesday, saying he hoped Republicans and President Barack Obama could "set differences aside" in the interest of helping ordinary Americans.
While not endorsing comprehensive immigration reforms backed by Obama, he did express openness on the subject in a speech to the American Enterprise Institute in Washington, saying he favored providing "an opportunity for legal residence and citizenship for those who were brought to this country as children and who know no other home."
That appeared to represent a reversal for Cantor, who in 2010 voted against the Dream Act, which would have cleared the way for such young people to remain in the United States.
"I'm pleased that many of my colleagues in both chambers of Congress on both sides of the aisle have begun work in good faith to address these issues," Cantor said.
Cantor gave little ground on any of the other differences between House Republicans and Obama in his speech, which his office billed as a major policy address.
Indeed, even as Cantor was speaking, Republican leaders and Obama were exchanging barbs in their latest standoff over deficit reduction, one likely to lead to $85 billion in damaging across-the-board budget cuts in March.
But the change in tone from one of the most partisan leaders of the House, who has helped lead the Republican charge against virtually everything Obama has proposed since taking office in 2009, was striking.
It followed months of rethinking among Republicans about their image among Americans following Obama's victory in the November election and their recent retreat from a battle they had looked forward to over the nation's borrowing limit.
Cantor made only passing reference to the bitter fights with Obama over "cliffs, debt ceilings and budgets" in which he has played such a visible role.
It is time, he said, to focus on "what lies beyond" them, including education, jobs, healthcare and innovation.
"Over the next two years, the House Majority will pursue an agenda based on a shared vision of creating the conditions for health, happiness and prosperity for more Americans and their families," Cantor said.
"....It is my hope that I can stand before you in two years and report back that our side, as well as the president's, found within us the ability to set differences aside, to provide relief to so many millions of Americans who simply want their lives to work again," Cantor said.
A Washington Post-ABC News/Washington poll last month found that 67 percent of Americans say that Republicans are doing "too little" to work with Obama.
The survey gave Republicans in Congress an approval rating of 24 percent, compared to a 37 percent rating for Democrats. Obama's approval recently hit a four-year high of 60 percent.
Cantor, 49, is widely seen as a possible successor to John Boehner, 63, as House Speaker, the chamber's top job.
While the two insist that they have a close working relationship, at times they have offered competing visions. On Tuesday, however, Boehner said they were on the same page.
Speaking with reporters after a meeting with House Republicans, Boehner said, "As I told the members, Eric's giving a very important speech."
"While there's a lot of focus on the deficit and debt, there are a lot of other things that Republicans plan to do over the course of this year," Boehner said.
"And if we're going to connect with the American people, it's important that they see, not only that we're serious about solving our debt problem, but we're serious about addressing issues like energy, like education, to show really the breath of the effort that we're involved in," Boehner added.
During the past two years, the White House has tried to make Cantor the face of congressional Republicans, and has made it clear that Obama prefers working with Boehner.
In an apparent effort to present a softer personal image, Cantor punctuated his prepared speech with references to a long lineup of people, including his wife and three children, his dad, a Baltimore nurse and a police officer from his hometown of Richmond, Virginia.
He spoke of visiting an inner-city school this week, and introduced a student from the school and his father to illustrate his interest in finding new solutions in education. (Editing by Fred Barbash and Eric Walsh)