[cnn-photo-caption image= http://i.cdn.turner.com/cnn/2008/images/06/04/art.obamacap.ap.jpg caption="Obama is back on Capitol Hill Wednesday."] WASHINGTON (CNN) - Barack Obama's run for the White House bodes well for the future, the presumptive Democratic nominee told CNN Wednesday, a day after he clinched the nomination.
"I have heard from a number of people already, both black and white, that their kids - 7, 8, 9 years old - take for granted now that, of course a black can run for president, that a woman can run for president," he said.
"There is a matter-of-factness to it that i think bodes well for the future."
The Illinois senator said it was "an enormous honor" and "very humbling" to be the first African-American to lead a major party ticket for president.
"You think about all the people who had to knock down barriers for me to walk through this door," he said in a Senate hallway. "And the challenges they went through were so much more difficult, so much more severe, and the risks they took were so much greater that I will say, last night standing in that auditorium, it struck me that it was testimony to them."
Obama dodged questions about Hillary Clinton, his rival for the Democratic nomination who has not admitted defeat.
They spoke by telephone Tuesday night and met briefly Wednesday in person at the annual conference of a pro-Israel lobbying group, the America-Israel Public Affairs Committee.
"It wasn't a detailed conversation," Obama said. "As I said, I am very confident about how we're going to be able to bring this party together."