Hillary Rodham Clinton and likely Democratic presidential nominee Barack Obama met privately to talk about uniting the Democratic Party, as pressure mounted for the Illinois senator to invite the former first lady to become his running mate. Obama said he will not be rushed into a decision on choosing a vice president. Clinton supporters in Congress and elsewhere promoted a "dream ticket," ramping up a campaign Thursday to persuade him to make her his No. 2. "Senator Clinton and Senator Obama met tonight and had a productive discussion about the important work that needs to be done to succeed in November," their campaigns said in joint statement. The statement included no details of their talks. Robert Gibbs, an Obama spokesman, would not say where the former rivals met, except that it was not at Clinton's home in Washington, as had been widely reported. He also declined to comment on their topics of discussion, including the possibility of Obama inviting Clinton to become his running mate. Clinton's campaign also was not commenting. The meeting between the two Democrats came hours after Clinton appeared to reject efforts by supporters urging Obama to choose her as his vice president, and promised to rally support for her one-time opponent in the general election. "She is not seeking the vice presidency, and no one speaks for her but her," Clinton's communication director Howard Wolfson said. "The choice here is Senator Obama's and his alone." However, Clinton has told lawmakers privately that she would be interested in the vice presidential nomination. Clinton was once seen as unbeatable for the Democratic presidential nomination, but her hopes of becoming the first woman US president faded as Obama chipped away at her early lead to become the first black presidential nominee from a major US party. She returned to Washington after the last primaries on Tuesday night, when Obama earned the 2,118 delegates he needed to secure the nomination. She planned to announce Saturday that she was ending her campaign and supporting Obama. After a divisive race marred by racism and sexism, Clinton starts her new role as an Obama booster with a lot of angry supporters. Their hard-fought battle sparked rifts that party leaders hope Clinton's public show of support could help heal. "I will be speaking on Saturday about how together we can rally the party behind Senator Obama," Clinton told supporters in an e-mail Thursday. "The stakes are too high and the task before us too important to do otherwise." Reporters traveling with Obama sensed something might be happening between the pair when they arrived at Dulles International Airport after an event in Northern Virginia and he was not aboard the airplane. Asked at the time about the Illinois senator's whereabouts, Gibbs smiled and declined to comment. Earlier Thursday, Obama told reporters his search for a running mate will be secret. He called it the most important decision he will make for the duration of his campaign. "I intend to do it right and I am not going to do it in the press," he said. "The next time you hear from me about the vice presidential selection process will be when I have selected a vice president." Obama has chosen a three-person team that includes Caroline Kennedy, the daughter of late President John F. Kennedy, to vet potential vice president candidates. If Obama made Clinton his running mate, it might help him tap into her core supporters, who have so far eluded him, including masses of blue-collar voters in swing states, Hispanics and older voters, especially women. Some of Clinton's closest supporters - the nearly two dozen Democrats in the House of Representatives from her home state of New York switched their allegiances to Obama on Thursday. The public announcement from the 23 in New York followed two days of private phone calls weighing her options. Another of Clinton's most prominent supporters, Ohio Gov. Ted Strickland, also announced his "wholehearted and enthusiastic support" for Obama on Thursday. Obama's general-election battle against Republican John McCain, a veteran senator who effectively clinched the Republican nomination in March, is likely to focus on Iraq and McCain's relationship with the unpopular President George W. Bush. The Illinois senator hit the ground running on the general election campaign trail against McCain in Virginia. The state has long voted for Republican presidential candidates, but Democrats believe they can swing it into their camp for the general election after several years of inroads fueled by the population-swelling in the more liberal northern area of the state. At a stop in Bristol, he criticized McCain, primarily over health care, and sought anew to link his Republican rival to Bush. "Now, I respect John McCain, and I honor his service to this country. My differences with him are not personal; they're about the policies he's proposed on this campaign - policies that are no different than the ones that have failed us for the last eight years," Obama said. Obama argued that health care premiums have risen faster than wages since Bush took office, and that millions more Americans are uninsured "yet John McCain actually wants to double down on the failed policies that have done so little to help ordinary Americans." Health care could become a major issue in the race in a country where about 40 million people are uninsured. Clinton's advisers said she also wants to make sure the issue remains primary; it is one of the few issues where she and Obama had substantive differences. Clinton favors an individual mandate requiring everyone to buy insurance; Obama has resisted such a requirement, calling it unenforceable and too expensive for many people. On his campaign plane, Obama praised Clinton for inspiring millions of voters and said she had opened the doors for his two young daughters to imagine being president one day. "We're going to speak to them but also listen to them and get advice," he said of Clinton's campaign team.