WASHINGTON (CNN) -- Sen. Barack Obama, the newly minted presumptive Democratic presidential nominee, said Wednesday it was "very humbling" to be the the first African-American to lead a major party's ticket and expressed confidence that the party would unify behind him.
"You think about all the people who had to knock down barriers for me to walk through this door," he said. "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."
The senator from Illinois also said his successful campaign for the Democratic presidential nomination has taught America's children that the Oval Office was within anyone's reach.
"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."
Asked if he was disappointed that his rival for the Democratic nomination, Sen. Hillary Clinton, did not concede outright Tuesday night, Obama said his priority was unifying the party.
Obama won the 2,118 delegates needed to capture the nomination after the primaries in South Dakota and Montana on Tuesday. The win came after five months of, at times, bitter contests with Clinton. He now has 2,158 delegates, according to CNN estimates.
"I just spoke to [Clinton] today, and we are going to be having a conversation in the coming weeks," Obama said Wednesday. "I am very confident how unified the Democratic Party is going to be to win in November." iReport.com: Obama/Clinton -- dream team or nightmare?
Clinton has not officially conceded, but her supporters and party leaders are already asking about her next move.
Both candidates were in Washington on Wednesday, first to each address the influential American Israel Public Affairs Committee, and later when they're expected in the Senate for a budget vote.
Obama and Clinton ran into each other at the AIPAC conference and had a brief chat, Obama spokeswoman Linda Douglass said.
"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."
Before the Israel lobbying group, Obama said of Clinton: "She's an extraordinary leader of the Democratic Party, and has made history alongside me over the last 16 months. I'm very proud to have competed
Not even 24 hours after becoming the presumptive Democratic nominee, Obama already faced questions as to who he would name as his running mate.
On Wednesday, Obama tapped a three-person team to vet vice presidential candidates. Washington insiders Jim Johnson, the former CEO of Fannie Mae, and Eric Holder, a deputy attorney general in the Clinton administration, will conduct the review as will Caroline Kennedy, daughter of former President John F. Kennedy and a prominent Obama supporter.
Obama has already been pressed by at least one Clinton supporter to offer her the vice presidential nomination in the name of party unity.
Billionaire businessman Bob Johnson, the founder of Black Entertainment Television and a close adviser and friend to Clinton, launched a campaign Wednesday to persuade Obama to offer her the No. 2 slot.
When speaking to reporters Wednesday afternoon, Obama dodged questions about Clinton. Robert Gibbs, Obama's communications director, said Obama and Clinton spoke by phone for a few minutes Wednesday, but Obama did not raise the issue of the vice presidency.
Gibbs said that the vice presidential search is "going to start now in a little bit more earnestness because we're the presumptive nominee" and that Obama "looked forward to sitting down with her when it makes sense for her" to talk about Clinton's plans. Watch Gibbs praise Clinton »
"She's been a tenacious competitor. She's accumulated a lot for this country, and we want to make sure that we're appealing to her voters and we're getting our voters out and talking to independents and disillusioned Republicans to put together the coalition that we need for November," Gibbs said.
On Wednesday Obama's next challenger Arizona Sen. John McCain, the presumptive Republican nominee, congratulated Obama for his victory and immediately challenged him to a series of 10 town hall meetings before the two parties' conventions in late August and September.
Speaking in Baton Rouge, Louisiana, McCain cited a 1963 agreement between President Kennedy and Barry Goldwater to hold such debates as part of the 1964 election campaign. Kennedy was assassinated before the campaign began.
"What a welcome change it would be were presidential candidates in our time to treat each other and the people they seek to lead with respect and courtesy as they discussed the great issues of the day, without the empty sound bites and media-filtered exchanges that dominate our elections," McCain said in a letter to Obama released by McCain's campaign.
Regular appearances with Obama could help McCain compensate for the Democrat's fundraising success by providing him regular free media exposure.
Obama said last month he would favor such debates.
"Obviously, we would have to think through the logistics on that," Obama said May 11 when the idea was floated. "But ... if I have the opportunity to debate substantive issues before the voters with John McCain, that's something that I am going to welcome."
