A top House Republican on Tuesday offered a new vision for his party, a kinder, gentler and more helpful version that he said could help Republicans to rebound from the losses they suffered in the presidential and Senate races last year.

Majority Leader Eric Cantor, in a speech to the conservative American Enterprise Institute, abandoned the GOP's usual talking points about slashing runaway federal spending, eliminating the debt and stopping the Democrats from raising taxes.

Instead, Cantor announced that House Republicans would begin pushing proposals dealing with education, health care, immigration and job growth, including student aid that would make college more affordable, flexible employment schedules in the private sector and job training for a changing workforce.

"Our goal," Cantor said, "is to ensure every American has a fair shot at earning their success and achieving their dreams."

The speech marked a major rebranding effort for the party at a time when polls show the public growing increasingly critical of the party, in particular its handling of spending standoffs with the White House, such as the recent "fiscal cliff" battle.

The party could become even less popular in the months ahead as additional spending fights loom and Congress begins debating immigration reform and gun control.

The GOP has strenuously resisted changes to the nation's immigration system and virtually every gun control measure that has been raised. But Cantor, the No. 2 Republican in the House and an influential voice within the party, changed course Tuesday.

Cantor endorsed allowing the children of illegal immigrants who were brought to the U.S. illegally to gain legal status, calling it "a good place to start" on immigration. Republicans have for years opposed similar proposals from President Obama and other Democrats.

Cantor on Tuesday also told CNN that he would back stricter background checks for gun buyers, something Obama has called for but the National Rifle Association and other pro-gun groups denounced as ineffective.

And before the start of the AEI speech, he told CNN that he supports stricter background checks for gun purchases, countering the viewpoint of anti-gun control groups and supporting Democrats and President Obama who are pushing for such a measure to pass Congress.

Cantor's speech didn't mark a complete break with Republican Party orthodoxy, however. He also endorsed creating school vouchers, eliminating taxes and fees imposed by Obama's health care reforms and simplifying the tax code.

On Capitol Hill, lawmakers in both parties praised Cantor's speech, particularly longtime members who viewed the 2012 election -- in which Republicans lost the White House and Senate seats -- as a warning sign that the party needs to change course.

"I do think we need to do a better job of telling people what we are for, not just what we are against, but what we are for," Rep. Mike Simpson, R-Idaho, told The Washington Examiner. "I just think we have let others define us, and we need to be defining ourselves."

Rep. Lamar Smith, R-Texas, said Cantor's speech "did a great job of laying out the agenda we need to follow, personalizing it and explaining how it is going to help the American people."

But others, like four-term Rep. Jim Jordan, R-Ohio, insist the party must remain focused on its conservative principles.

"Strong national defense, lower taxes, less spending and defending traditional values," Jordan said. "When we effectively communicate that, we win."