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By Eun Kyung Kim

President Obama expressed confidence in passage of a bill that would make major changes to the nation’s immigration system, in an exclusive TODAY interview conducted days before key senators introduced sweeping legislation on the issue.

Obama credited the work of a bipartisan “Group of Eight” senators for helping to push the issue through Capitol Hill. On Tuesday, he signed off on an immigration plan during a White House meeting with the legislation’s top sponsors, Democrat Charles Schumer and Republican John McCain.

During a wide-ranging interview earlier in the week with TODAY’s Savannah Guthrie, the president said he hopes the group’s work will set the tone for lawmakers working on other contentious issues.

“My hope is not only that we end up with an immigration bill that shows that we're a nation of laws and a nation of citizens, that helps our economic growth, that helps us attract incredible talent to our shores,” he said. “But I also hope that it kind of restarts muscle memory in Congress for getting bipartisan legislation done.”

On gun control, Obama said he feels responsible to keep pushing the issue so that mass shootings like the one at Sandy Hook Elementary School don’t happen again.

“I feel personally responsible the same way I hope every parent out there feels responsible for all our kids,” he said. “The key thing for me, is every once in a while we are confronted with an issue that should transcend politics.”

Obama’s discussion was recorded just hours before two bombs exploded Monday at the Boston Marathon. The first of the two-part interview, in which the president covered North Korea, gun control legislation and the fight over the nation’s budget, aired Tuesday.

The president said the media has portrayed lawmakers as a group far more polarized than they actually are.

“I think the political engines of the party and blogs, et cetera, force people into taking more extreme positions publicly than they actually believe privately,” he said. “I’m willing to try anything. As I’ve said, I'm willing to wash folks' cars and walk their dogs if I can get some legislation passed.”

Obama also answered questions about whether his dinner diplomacy strategy has helped open the dialogue with Republicans over issues such as immigration, gun control and the federal budget.

“I don’t know about my charms, but they’ve been useful conversations,” Obama said about the White House dinner party, the second of which he hosted last week.

Obama weighed in briefly on the trial of Philadelphia abortion doctor Kermit Gosnell, saying he was “familiar” with the case but wouldn’t comment directly because it was active. Gosnell is accused in the deaths of seven allegedlyviable fetuses and a pregnant woman.

“If an individual carrying out an abortion, operating a clinic or doing anything else is violating medical ethics, violating the law then they should be prosecuted,” Obama said.

But he also clarified his own views on the controversial issue.

“I think President Clinton said it pretty well when he said, ‘Abortion should be safe, legal and rare,’” he said.

Obama also addressed the criticism he received earlier this month at a political fundraiser when he called California’s Kamala Harris the “best looking attorney general.” The president said that although “Kamala knew where I was coming from,” he took his joke with his long-time friend too far.

“I do think it was a useful teaching moment for me and for the country,” he said. “As the father of two daughters I want to make sure that they're judged on the merits and not on their appearance.”

Watch video: 'My best-looking' quip was 'teaching moment'

Obama later called Harris to apologize for the comment.

“I've got no problem in people, I think, using what was intended as an innocuous comment to make this larger point that we want to make sure that women are judged based on the job they do and not how they look,” he said.

Obama also was asked about Hillary Clinton, his “extraordinary former secretary of state and a potential presidential candidate in 2016. He declined to comment on his hopes for her entering that race.

Watch video: Obama addresses 2016, Hillary Clinton

“She’s earned a rest,” he said. “And I know that she's going to be able, whatever she does, to continue to be a leader and incredibly positive force for the causes I care about and that she cares about all around the world.”

Obama also provided clarity on the matter of who cleared a trip musicians Jay-Z and Beyonce took recently to Cuba.

Although Jay-Z wrote in lyrics to a new rap that Obama gave him the green light for the trip, White House recently said the Treasury Department handles such matters.

Watch video: Beyonce and Jay-Z's Cuba trip was sanctioned

The president confirmed that.

“I wasn’t familiar that they were taking the trip. My understanding is I think they went through a group that organizes these educational trips down to Cuba,” he said. “You know, this is not something the White House was involved with. We've got better things to do.”